Maths-
General
Easy

Question

Surface area of a cube is 443.76 cm2 . Find the volume of it?

  1. 7.6
  2. 8.4
  3. 8.6
  4. 6.4

Hint:

 Volume of a cube = (side)3  [cubic units]
Total Surface Area(TSA) of cube = 6a2
Where,   a is side of cube

The correct answer is: 6.4


    • We are given that 
    Surface area of a cube = 443.76 cm2
    • We have to find volume of the cube
    6a2 = 443.76
    • Divide both sides of equation by 6
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a squared equals fraction numerator 443.76 over denominator 6 end fraction end cell row cell a squared equals 73.96 end cell end table
    • Taking square root of both sides we get,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell a equals square root of 73.96 end root end cell row cell a equals 8.6 end cell end table
    • Therefore, the volume of the given cube is
    Volume = a3 = (8.6)3
    Volume = 636.056 cm3
    • The approximate of the volume is 6.4 from the given options,
    • Therefore the correct option is d) 6.4.

    Related Questions to study

    General
    Maths-

    Find the volume of the cone. Round decimals nearest tenth r = 14ft, h = 18 ft

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Radius , r = 14 ft
    Height , h = 18 ft
    We have to find the volume of the given cone
    We know that
    Volume of a cone = (1 third)πr2h
    = (1 third)(3.14)(14 x 14)(18)
    = (1 third)(3.14) (196 x 18)
    = (1 third)(3.14)(3528)
    = 11077.9 / 3
    = 3692.6 ft3
    Therefore correct option is b) 3692.6 ft3.

    Find the volume of the cone. Round decimals nearest tenth r = 14ft, h = 18 ft

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Radius , r = 14 ft
    Height , h = 18 ft
    We have to find the volume of the given cone
    We know that
    Volume of a cone = (1 third)πr2h
    = (1 third)(3.14)(14 x 14)(18)
    = (1 third)(3.14) (196 x 18)
    = (1 third)(3.14)(3528)
    = 11077.9 / 3
    = 3692.6 ft3
    Therefore correct option is b) 3692.6 ft3.
    General
    Maths-

    The dimensions of a cuboid are in the ratio of 4:3:2 and its total surface area is 1300 cm2 . Find its length, breadth, and height respectively?

    Given: Ratio of dimensions of a cuboid is 4:3:2 & The Total surface area of cuboid is 1300 cm².
    We have to find Length, breadth & height of cuboid.
    • Let length, breadth and height of cuboid be 4x, 3x and 2x respectively.⠀⠀
    • Now, As we know that, total surface area of cuboid is given by,
    Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
    where, l, b & h are length, breadth and height of cuboid respectively.
    • We have , length = 4x
    Breadth, b = 3x
    Height, h = 2x
    TSA = 1300 cm2
    • Putting the values in the formula
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 left square bracket left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 3 x right parenthesis left parenthesis 2 x right parenthesis plus left parenthesis 2 x right parenthesis left parenthesis 4 x right parenthesis right square bracket equals 1300 end cell row cell 2 open square brackets 12 x squared plus 6 x squared plus 8 x squared close square brackets equals 1300 end cell row cell 2 open parentheses 26 x squared close parentheses equals 1300 end cell end table
    • Dividing both sides of equation by 2      
    •  table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 26 x squared equals 1300 over 2 end cell row cell 26 x squared equals 650 end cell end table
    • Dividing both sides of equation by 26
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals 650 over 26 end cell row cell x squared equals 25 end cell row cell x equals square root of 25 end cell row cell x equals 5 end cell end table
    Therefore,
    The dimensions of cuboid are,
    Length = 4x = 4(5)= 20
    Breadth= 3x = 3(5) =15
    Height = 2x=2(5)= 10
    thereforeThus, The length, breadth & height of cuboid are 20 cm, 15 cm & 10 cm respectively.
    Therefore the correct option is d) 20 cm,15cm , 10 cm

    The dimensions of a cuboid are in the ratio of 4:3:2 and its total surface area is 1300 cm2 . Find its length, breadth, and height respectively?

    Maths-General
    Given: Ratio of dimensions of a cuboid is 4:3:2 & The Total surface area of cuboid is 1300 cm².
    We have to find Length, breadth & height of cuboid.
    • Let length, breadth and height of cuboid be 4x, 3x and 2x respectively.⠀⠀
    • Now, As we know that, total surface area of cuboid is given by,
    Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
    where, l, b & h are length, breadth and height of cuboid respectively.
    • We have , length = 4x
    Breadth, b = 3x
    Height, h = 2x
    TSA = 1300 cm2
    • Putting the values in the formula
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 2 left square bracket left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 3 x right parenthesis left parenthesis 2 x right parenthesis plus left parenthesis 2 x right parenthesis left parenthesis 4 x right parenthesis right square bracket equals 1300 end cell row cell 2 open square brackets 12 x squared plus 6 x squared plus 8 x squared close square brackets equals 1300 end cell row cell 2 open parentheses 26 x squared close parentheses equals 1300 end cell end table
    • Dividing both sides of equation by 2      
    •  table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell 26 x squared equals 1300 over 2 end cell row cell 26 x squared equals 650 end cell end table
    • Dividing both sides of equation by 26
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell x squared equals 650 over 26 end cell row cell x squared equals 25 end cell row cell x equals square root of 25 end cell row cell x equals 5 end cell end table
    Therefore,
    The dimensions of cuboid are,
    Length = 4x = 4(5)= 20
    Breadth= 3x = 3(5) =15
    Height = 2x=2(5)= 10
    thereforeThus, The length, breadth & height of cuboid are 20 cm, 15 cm & 10 cm respectively.
    Therefore the correct option is d) 20 cm,15cm , 10 cm
    General
    Maths-

    Find the volume of the cone. Round decimals nearest tenth. D = 12cm, h = 8 cm

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Diameter = 12 cm
    Radius, r = 12 over 2 = 6 cm
    Height, h = 8 cm
    We have to find the volume of the given cone
    We know that
    Volume of a cone = (1 third)πr2h
    = (1 third)(3.14)(6 x 6) (8)
    = (1 third)(3.14) (36 x 8)
    = (1 third)(3.14)(288)
    = 904.32 over 3
    = 301.4 cm3
    Therefore correct option is c) 301.4 cm3.

    Find the volume of the cone. Round decimals nearest tenth. D = 12cm, h = 8 cm

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Diameter = 12 cm
    Radius, r = 12 over 2 = 6 cm
    Height, h = 8 cm
    We have to find the volume of the given cone
    We know that
    Volume of a cone = (1 third)πr2h
    = (1 third)(3.14)(6 x 6) (8)
    = (1 third)(3.14) (36 x 8)
    = (1 third)(3.14)(288)
    = 904.32 over 3
    = 301.4 cm3
    Therefore correct option is c) 301.4 cm3.
    parallel
    General
    Maths-

    a squared minus 2 a b plus b squared equals

    Hint :- Divide the mid term as a product of 1st and 3rd elements and take common elements out.
    Ans:- Option B
    Explanation:-
    Given, a squared minus 2 a b plus b squared
    Divide -2ab into -ab and -ab so that (-ab)(-ab) =  open parentheses a squared close parentheses open parentheses b squared close parentheses we get a squared minus a b minus a b plus b squared
    Taking common elements we get  a left parenthesis a minus b right parenthesis minus b left parenthesis a minus b right parenthesis
    Taking (a-b) common gives left parenthesis a minus b right parenthesis left parenthesis a minus b right parenthesis equals left parenthesis a minus b right parenthesis squared
    ∴ Option B is correct

    a squared minus 2 a b plus b squared equals

    Maths-General
    Hint :- Divide the mid term as a product of 1st and 3rd elements and take common elements out.
    Ans:- Option B
    Explanation:-
    Given, a squared minus 2 a b plus b squared
    Divide -2ab into -ab and -ab so that (-ab)(-ab) =  open parentheses a squared close parentheses open parentheses b squared close parentheses we get a squared minus a b minus a b plus b squared
    Taking common elements we get  a left parenthesis a minus b right parenthesis minus b left parenthesis a minus b right parenthesis
    Taking (a-b) common gives left parenthesis a minus b right parenthesis left parenthesis a minus b right parenthesis equals left parenthesis a minus b right parenthesis squared
    ∴ Option B is correct
    General
    Maths-

    Find out the side of cube if the complete surface area is given to be 346.56 cm2.

    • Step 1:We have given the total surface area of the cube.
    Area = 346.56 cm2
    • Step 2: We know that
    Surface Area = 6a2
                                                                                   346.56 = 6a2
    • ·          Step 3: For finding the side firstly divide both sides if equation by 6
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator 346.56 over denominator 6 end fraction equals a squared end cell row cell 57.76 equals a squared end cell end table
    • Step 4:- Taking square root of both sides we get,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell square root of 57.76 end root equals a end cell row cell 7.6 equals a end cell end table
    • ·          Step 5: Therefore, the length of side of the given cube is 7.6 cm2.
      • Therefore, the correct answer is option B) 7.6 cm.

    Find out the side of cube if the complete surface area is given to be 346.56 cm2.

    Maths-General
    • Step 1:We have given the total surface area of the cube.
    Area = 346.56 cm2
    • Step 2: We know that
    Surface Area = 6a2
                                                                                   346.56 = 6a2
    • ·          Step 3: For finding the side firstly divide both sides if equation by 6
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator 346.56 over denominator 6 end fraction equals a squared end cell row cell 57.76 equals a squared end cell end table
    • Step 4:- Taking square root of both sides we get,
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell square root of 57.76 end root equals a end cell row cell 7.6 equals a end cell end table
    • ·          Step 5: Therefore, the length of side of the given cube is 7.6 cm2.
      • Therefore, the correct answer is option B) 7.6 cm.
    General
    Maths-

    Find the volume of the cone. Use 3.14 for π. Round decimal answers to the nearest tenth. r= 4 in, height = 4 in

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Radius, r = 4 in
    Height, h = 4 in
    We have to find the volume of the given cone
    We know that
    Volume of a cone = (1 third)πr2h
    = (1 third)(3.14)(4 x 4) (4)
    = (1 third)(3.14) (16 x 4)
    = (1 third)(3.14)(64)
    = 200.96 over 3
    = 66.9 in3
    Therefore correct option is b) 66.9 in3.

    Find the volume of the cone. Use 3.14 for π. Round decimal answers to the nearest tenth. r= 4 in, height = 4 in

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Radius, r = 4 in
    Height, h = 4 in
    We have to find the volume of the given cone
    We know that
    Volume of a cone = (1 third)πr2h
    = (1 third)(3.14)(4 x 4) (4)
    = (1 third)(3.14) (16 x 4)
    = (1 third)(3.14)(64)
    = 200.96 over 3
    = 66.9 in3
    Therefore correct option is b) 66.9 in3.
    parallel
    General
    Maths-

    Calculate the LSA of a cuboid of ,length = 40cm ,breadth = 20cm and height = 10cm.

    • We are given the dimensions of cuboid.
    length = 40cm = l
    breadth = 20cm = b
    height = 10cm = h
    • We will calculate the LSA of given cuboid
    We know that,
    The Lateral Surface area of cuboid = 2h( l + b)
    • By using the above formula of the lateral surface area of the cuboid, we get
    The lateral surface area of the given cuboid is,

    = 2h( l + b)

    = 2 cross times 10 cross times (40 + 20)

    = 20 cross times (60)

    LSA= 1200 cm2
    Therefore the Lateral surface area of the given cuboid is 1200 cm2.
    The correct answer is option d) 1200.

    Calculate the LSA of a cuboid of ,length = 40cm ,breadth = 20cm and height = 10cm.

    Maths-General
    • We are given the dimensions of cuboid.
    length = 40cm = l
    breadth = 20cm = b
    height = 10cm = h
    • We will calculate the LSA of given cuboid
    We know that,
    The Lateral Surface area of cuboid = 2h( l + b)
    • By using the above formula of the lateral surface area of the cuboid, we get
    The lateral surface area of the given cuboid is,

    = 2h( l + b)

    = 2 cross times 10 cross times (40 + 20)

    = 20 cross times (60)

    LSA= 1200 cm2
    Therefore the Lateral surface area of the given cuboid is 1200 cm2.
    The correct answer is option d) 1200.

    General
    Maths-

    The diameter of the ends of a bucket of height 24 cm are 42 cm and 14 cm
    respectively .Find the capacity of the bucket

    Hint:- Volume of frustum of cone = fraction numerator pi h over denominator 3 end fraction open square brackets fraction numerator open parentheses R cubed minus r cubed close parentheses over denominator R minus r end fraction close square brackets
    Solution:- We have given the dimensions of a bucket which is of frustrum shape
    Top diameter = 42 cm
    Top radius, R = 21 cm
    Bottom diameter = 14
    Bottom radius, r = 7 cm
    Height of frustrum , h = 24 cm
    Therefore capacity of bucket = volume of bucket
    equals fraction numerator pi h over denominator 3 end fraction open square brackets fraction numerator open parentheses R cubed minus r cubed close parentheses over denominator R minus r end fraction close square brackets
    equals fraction numerator left parenthesis 22 divided by 7 right parenthesis left parenthesis 24 right parenthesis over denominator 3 end fraction open square brackets fraction numerator open parentheses 21 cubed minus 7 cubed close parentheses over denominator 21 minus 7 end fraction close square brackets
    left parenthesis 22 right parenthesis left parenthesis 8 right parenthesis open square brackets fraction numerator open parentheses 21 cubed minus 7 cubed close parentheses over denominator 7 cross times 14 end fraction close square brackets
    left parenthesis 176 right parenthesis open square brackets fraction numerator left parenthesis 9261 minus 343 right parenthesis over denominator 98 end fraction close square brackets
    left parenthesis 176 right parenthesis open square brackets fraction numerator left parenthesis 8918 right parenthesis over denominator 98 end fraction close square brackets
    = 176 × 91
    16016 cm cubed
    Therefore, the correct option is a)16016 cm3

    The diameter of the ends of a bucket of height 24 cm are 42 cm and 14 cm
    respectively .Find the capacity of the bucket

    Maths-General
    Hint:- Volume of frustum of cone = fraction numerator pi h over denominator 3 end fraction open square brackets fraction numerator open parentheses R cubed minus r cubed close parentheses over denominator R minus r end fraction close square brackets
    Solution:- We have given the dimensions of a bucket which is of frustrum shape
    Top diameter = 42 cm
    Top radius, R = 21 cm
    Bottom diameter = 14
    Bottom radius, r = 7 cm
    Height of frustrum , h = 24 cm
    Therefore capacity of bucket = volume of bucket
    equals fraction numerator pi h over denominator 3 end fraction open square brackets fraction numerator open parentheses R cubed minus r cubed close parentheses over denominator R minus r end fraction close square brackets
    equals fraction numerator left parenthesis 22 divided by 7 right parenthesis left parenthesis 24 right parenthesis over denominator 3 end fraction open square brackets fraction numerator open parentheses 21 cubed minus 7 cubed close parentheses over denominator 21 minus 7 end fraction close square brackets
    left parenthesis 22 right parenthesis left parenthesis 8 right parenthesis open square brackets fraction numerator open parentheses 21 cubed minus 7 cubed close parentheses over denominator 7 cross times 14 end fraction close square brackets
    left parenthesis 176 right parenthesis open square brackets fraction numerator left parenthesis 9261 minus 343 right parenthesis over denominator 98 end fraction close square brackets
    left parenthesis 176 right parenthesis open square brackets fraction numerator left parenthesis 8918 right parenthesis over denominator 98 end fraction close square brackets
    = 176 × 91
    16016 cm cubed
    Therefore, the correct option is a)16016 cm3
    General
    Maths-

    Given LSA of a cuboid is 900cm2 and the breadth x length are 10cm x 20cm.Calculate height of cuboid.

    • We have given,
    LSA of cuboid = 900cm2
    Breadth= 10 cm
    Length = 20 cm
    • We know that ,
    LSA of cuboid = 2h( l + b)
    • Insert the values in the above equation.
    900 = 2h (20 + 10)
    900 = 2h(30)
    Divide both sides of equation by 30, we get
    table attributes columnspacing 1em end attributes row cell 900 over 30 equals 2 h end cell row cell 30 equals 2 h end cell end table
    Divide both sides of equation by 2, we get
    h = 15
    • Therefore the height of given cuboid is 15 cm.
    • The correct option is option a) 15 .

    Given LSA of a cuboid is 900cm2 and the breadth x length are 10cm x 20cm.Calculate height of cuboid.

    Maths-General
    • We have given,
    LSA of cuboid = 900cm2
    Breadth= 10 cm
    Length = 20 cm
    • We know that ,
    LSA of cuboid = 2h( l + b)
    • Insert the values in the above equation.
    900 = 2h (20 + 10)
    900 = 2h(30)
    Divide both sides of equation by 30, we get
    table attributes columnspacing 1em end attributes row cell 900 over 30 equals 2 h end cell row cell 30 equals 2 h end cell end table
    Divide both sides of equation by 2, we get
    h = 15
    • Therefore the height of given cuboid is 15 cm.
    • The correct option is option a) 15 .
    parallel
    General
    Maths-

    Factor the given expression completely.
    negative 3 x cubed plus 18 x squared minus 27 x

    HINT :- using the formula a squared minus 2 a b plus b squared equals left parenthesis a minus b right parenthesis squared factorize the given expression
    Ans:- 3 x left parenthesis x minus 3 right parenthesis squared is the factorized form of the given expression.
    Explanation :-
    Given, negative 3 x cubed plus 18 x squared minus 27 x
    Taking out common factor -3x out of equation , we get negative 3 x open parentheses x squared minus 6 x plus 9 close parentheses
    Write 6 x text  as  end text 2 left parenthesis 3 right parenthesis x text  and  end text 9 text  as  end text left parenthesis 3 right parenthesis squared text  we get  end text minus 3 x open parentheses x squared minus 2 left parenthesis 3 right parenthesis x plus 3 squared close parentheses
    Applying a squared minus 2 a b plus b squared equals left parenthesis a minus b right parenthesis squared
    Here a = x ; b = 3
    We get , negative 3 x cubed plus 18 x squared minus 27 x equals negative 3 x left parenthesis x minus 3 right parenthesis squared
    negative 3 x left parenthesis x minus 3 right parenthesis squared is the factorized form of the given expression.

    Factor the given expression completely.
    negative 3 x cubed plus 18 x squared minus 27 x

    Maths-General
    HINT :- using the formula a squared minus 2 a b plus b squared equals left parenthesis a minus b right parenthesis squared factorize the given expression
    Ans:- 3 x left parenthesis x minus 3 right parenthesis squared is the factorized form of the given expression.
    Explanation :-
    Given, negative 3 x cubed plus 18 x squared minus 27 x
    Taking out common factor -3x out of equation , we get negative 3 x open parentheses x squared minus 6 x plus 9 close parentheses
    Write 6 x text  as  end text 2 left parenthesis 3 right parenthesis x text  and  end text 9 text  as  end text left parenthesis 3 right parenthesis squared text  we get  end text minus 3 x open parentheses x squared minus 2 left parenthesis 3 right parenthesis x plus 3 squared close parentheses
    Applying a squared minus 2 a b plus b squared equals left parenthesis a minus b right parenthesis squared
    Here a = x ; b = 3
    We get , negative 3 x cubed plus 18 x squared minus 27 x equals negative 3 x left parenthesis x minus 3 right parenthesis squared
    negative 3 x left parenthesis x minus 3 right parenthesis squared is the factorized form of the given expression.

    Find the height of a cuboid whose base area is 180cm2 and volume is 900cm2

    Maths-General
    Volume of cuboid = Base area × Height  [Cubic units]
    The base of the cuboid is rectangle in shape. So, the base area of a cuboid is equal to the product of its length and breadth. Hence,
    Volume of a cuboid = length × breadth × height    [cubic units]
    or
    Volume of a cuboid = l × b × h    [cubic units]
    Where,
    • l = length
    • b = breadth
    • h = height
    Solution:-
    • We have given that,
    Base area of cuboid = length × breadth = 180 cm²
    Volume of cuboid = length × breadth × height = 900 cm³
    • We will get,
    Volume of a cuboid = Base area of cuboid × height of the cuboid
    900 cm³ = 180 cm² × height
    • On dividing both sides by 180 we get,
    height = 900 over 180 = 5 cm
    Thus, the height of the cuboid is 5 cm.
    The correct option is c) 5 cm .
    General
    Maths-

    A cone has a circular base of radius 6m and volume 84π m³. The height of cone is

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Radius , r = 6 m
    Volume of cone = 84π m³
    We have to find the height of the given cone
    Let height of the cone be h
    We know that
    Volume of a cone = (1 third)πr2h
    84π = (1 third) π (6 x 6) (h)
    Divide both sides of equation by π
    84 = (2 x 6) (h)
    84 = 12h)
    h = 84 over 12
    h = 7 m
    Therefore correct option is a) 7m

    A cone has a circular base of radius 6m and volume 84π m³. The height of cone is

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Radius , r = 6 m
    Volume of cone = 84π m³
    We have to find the height of the given cone
    Let height of the cone be h
    We know that
    Volume of a cone = (1 third)πr2h
    84π = (1 third) π (6 x 6) (h)
    Divide both sides of equation by π
    84 = (2 x 6) (h)
    84 = 12h)
    h = 84 over 12
    h = 7 m
    Therefore correct option is a) 7m
    parallel
    General
    Maths-

    What is the factored form of  50 x squared minus 32 y squared ?

    HINT :- using the formula  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis factorize the given expression
    Ans:- 2 (5x + 4)(5x - 4) is the factorized form of the given expression.
    Explanation :-
    Given,50 x squared minus 32 y squared
    Taking out common factor 2 out of equation , we get 2 open parentheses 25 x squared minus 16 y squared close parentheses
    Write 25 x squared text  as  end text left parenthesis 5 x right parenthesis squared text  and  end text 16 y squared text  as  end text left parenthesis 4 y right parenthesis squared text  we get  end text 2 open parentheses left parenthesis 5 x right parenthesis squared minus left parenthesis 4 y right parenthesis squared close parentheses
    Applying  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    We get , 50 x squared minus 32 y squared equals 2 left parenthesis 5 x plus 4 y right parenthesis left parenthesis 5 x minus 4 y right parenthesis
    ∴ 2(5x+4y)(5x-4y) is the factorized form of the given expression.

    What is the factored form of  50 x squared minus 32 y squared ?

    Maths-General
    HINT :- using the formula  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis factorize the given expression
    Ans:- 2 (5x + 4)(5x - 4) is the factorized form of the given expression.
    Explanation :-
    Given,50 x squared minus 32 y squared
    Taking out common factor 2 out of equation , we get 2 open parentheses 25 x squared minus 16 y squared close parentheses
    Write 25 x squared text  as  end text left parenthesis 5 x right parenthesis squared text  and  end text 16 y squared text  as  end text left parenthesis 4 y right parenthesis squared text  we get  end text 2 open parentheses left parenthesis 5 x right parenthesis squared minus left parenthesis 4 y right parenthesis squared close parentheses
    Applying  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    We get , 50 x squared minus 32 y squared equals 2 left parenthesis 5 x plus 4 y right parenthesis left parenthesis 5 x minus 4 y right parenthesis
    ∴ 2(5x+4y)(5x-4y) is the factorized form of the given expression.
    General
    Maths-

    Find the slant height of the right circular cone if the base diameter of the right circular cone is 14 cm and the height is 24 cm.

    Hint:- Slant height L = square root of h squared plus r squared end root
    where h is height
    r is radius of base of cone

    Solution:- We have given the dimensions of a right circular cone
    Base diameter = 14 cm
    Radius, r = 14 over 2 = 7 cm
    Height, h = 24 cmsquare root of 625
    Let us find the slant height
    L = square root of h squared plus r squared end root
    L = square root of 24 squared plus 7 squared end root
    square root of 576 plus 49 end root
    square root of 625
    L = 25 cm
    Therefore, the correct option is d) 25 cm.

    Find the slant height of the right circular cone if the base diameter of the right circular cone is 14 cm and the height is 24 cm.

    Maths-General
    Hint:- Slant height L = square root of h squared plus r squared end root
    where h is height
    r is radius of base of cone

    Solution:- We have given the dimensions of a right circular cone
    Base diameter = 14 cm
    Radius, r = 14 over 2 = 7 cm
    Height, h = 24 cmsquare root of 625
    Let us find the slant height
    L = square root of h squared plus r squared end root
    L = square root of 24 squared plus 7 squared end root
    square root of 576 plus 49 end root
    square root of 625
    L = 25 cm
    Therefore, the correct option is d) 25 cm.
    General
    Maths-

    Factor the given expression completely.
    64 x squared y squared minus 144 z squared

    HINT :- using the formula a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis factorize the given expression
    Ans:- 16 (2xy + 3z) (2xy - 3z) is the factorized form of the given expression.
    Explanation :-
    Given, 64 x squared y squared minus 144 z squared
    Taking out common factor 16 out of equation , we get 16 open parentheses 4 x squared y squared minus 9 z squared close parentheses
    Write 4 x squared y squared text  as  end text left parenthesis 2 x y right parenthesis squared text  and  end text 9 z squared text  as  end text left parenthesis 3 z right parenthesis squared text  we get  end text 16 open parentheses left parenthesis 2 x y right parenthesis squared minus left parenthesis 3 z right parenthesis squared close parentheses
    Applying a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    Here a = 2xy ; b = 3z
    We get , 64 x squared y squared minus 144 z squared equals 16 left parenthesis 2 x y plus 3 z right parenthesis left parenthesis 2 x y minus 3 z right parenthesis
    ∴ 16 ( 2xy + 3z ) ( 2xy - 3z ) is the factorized form of the given expression.

    Factor the given expression completely.
    64 x squared y squared minus 144 z squared

    Maths-General
    HINT :- using the formula a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis factorize the given expression
    Ans:- 16 (2xy + 3z) (2xy - 3z) is the factorized form of the given expression.
    Explanation :-
    Given, 64 x squared y squared minus 144 z squared
    Taking out common factor 16 out of equation , we get 16 open parentheses 4 x squared y squared minus 9 z squared close parentheses
    Write 4 x squared y squared text  as  end text left parenthesis 2 x y right parenthesis squared text  and  end text 9 z squared text  as  end text left parenthesis 3 z right parenthesis squared text  we get  end text 16 open parentheses left parenthesis 2 x y right parenthesis squared minus left parenthesis 3 z right parenthesis squared close parentheses
    Applying a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    Here a = 2xy ; b = 3z
    We get , 64 x squared y squared minus 144 z squared equals 16 left parenthesis 2 x y plus 3 z right parenthesis left parenthesis 2 x y minus 3 z right parenthesis
    ∴ 16 ( 2xy + 3z ) ( 2xy - 3z ) is the factorized form of the given expression.

    parallel

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