Maths-
General
Easy

Question

Internal length, height, and breadth of an open box are 95 cm, 82 cm, and 75 cm. Thickness of wood is given to be 2.5 cm, calculate the cost of painting outside the box as Rs 1 per dm2

  1. 458.20
  2. 386.20
  3. 626.20
  4. 384.20

Hint:

 Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
Where,
l = length
b = breadth
h = height
We have to add the thickness of wood on both sides for finding the outside dimensions.

The correct answer is: 384.20


    We have given the Internal dimensions of the box
    length = 95 cm,
    breadth = 75 cm
    height = 82 cm
    Outer dimensions of the box are
    length = 95 + 2 cross times 2.5 = 100 cm,
    breadth = 75 + 2 cross times 2.5 = 80 cm
    height = 82 + 2.5 = 84.5 --as the box is open we will add only 2.5
    Surface area of the box = 2(lb+ bh +lh)

    = 2((95)(75)+(75)(82)+(95)(82))

    = 2(8000+6760+8450)=

    = 46420 cm2
    Surface area of the open box = Total area  - area of open side

    = 46420 – (95)(75)

    = 46420-8000

    = 38420 cm2

    = 384.2 dm2

    Cost of painting = Rs. 384.20
    Therefore option d) 384.20 is correct.

    Related Questions to study

    General
    Maths-

    The total surface area of a cube is 846 cm2. Find the height, breadth, and length if the dimensions are in the ratio of 3:4:5

    We have given the surface area of cube = 846cm2
    And the ratio of height breadth and length is 3:4:5
    Let , height = 3x,
    Breadth =4x,
    Length = 5x
    Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
    2 left square bracket left parenthesis 5 x right parenthesis left parenthesis 4 x right parenthesis plus left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 5 x right parenthesis left parenthesis 3 x right parenthesis right square bracket equals 846

    2 open square brackets 20 x squared plus 12 x squared plus 15 x squared close square brackets equals 846
    2(47x2) = 846
    Divide both sides by 2,
    table attributes columnspacing 1em end attributes row cell 47 x squared equals 846 over 2 end cell row cell 47 x squared equals 423 end cell end table
    Divide both sides by 47,
    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 423 over 47 end cell row cell x squared equals 9 end cell end table
    Taking square root
    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 equals square root of 9 end cell row cell x equals 3 end cell end table
    The dimensions of cuboid are,

    Height = 3x=3(3)= 9

    Breadth= 4x =4(3) =12

    Length = 5x = 5(3)= 15
    Therefore the option a)15cm , 12cm , 9cm is correct.

    The total surface area of a cube is 846 cm2. Find the height, breadth, and length if the dimensions are in the ratio of 3:4:5

    Maths-General
    We have given the surface area of cube = 846cm2
    And the ratio of height breadth and length is 3:4:5
    Let , height = 3x,
    Breadth =4x,
    Length = 5x
    Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
    2 left square bracket left parenthesis 5 x right parenthesis left parenthesis 4 x right parenthesis plus left parenthesis 4 x right parenthesis left parenthesis 3 x right parenthesis plus left parenthesis 5 x right parenthesis left parenthesis 3 x right parenthesis right square bracket equals 846

    2 open square brackets 20 x squared plus 12 x squared plus 15 x squared close square brackets equals 846
    2(47x2) = 846
    Divide both sides by 2,
    table attributes columnspacing 1em end attributes row cell 47 x squared equals 846 over 2 end cell row cell 47 x squared equals 423 end cell end table
    Divide both sides by 47,
    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 423 over 47 end cell row cell x squared equals 9 end cell end table
    Taking square root
    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 equals square root of 9 end cell row cell x equals 3 end cell end table
    The dimensions of cuboid are,

    Height = 3x=3(3)= 9

    Breadth= 4x =4(3) =12

    Length = 5x = 5(3)= 15
    Therefore the option a)15cm , 12cm , 9cm is correct.

    General
    Maths-

    A cube of 11 cm edge is immersed completely in a rectangular vessel containing the liquid. If the dimensions of the base of the vessel are 12 cm and 15 cm, calculate the rise in the water level?

    • We know that,
    The dimensions of the base of the vessel are 15 cm × 12 cm
    l =15cm
    b = 12cm
    • Consider the rise in the water level = h cm
    • Volume of given cube = (11)3=1331
    • So the volume of cube = volume of the vessel
    • Substituting these values

    1331 = 15 × 12 × h

    • By further calculation

    h = 1331/ (15 × 12)

    • So we get

    h = 1331/ 180 = 7.39 cm

    • Therefore, the rise in the water level is 7.39 cm.
    • Therefore the correct option is b)7.39.

    A cube of 11 cm edge is immersed completely in a rectangular vessel containing the liquid. If the dimensions of the base of the vessel are 12 cm and 15 cm, calculate the rise in the water level?

    Maths-General
    • We know that,
    The dimensions of the base of the vessel are 15 cm × 12 cm
    l =15cm
    b = 12cm
    • Consider the rise in the water level = h cm
    • Volume of given cube = (11)3=1331
    • So the volume of cube = volume of the vessel
    • Substituting these values

    1331 = 15 × 12 × h

    • By further calculation

    h = 1331/ (15 × 12)

    • So we get

    h = 1331/ 180 = 7.39 cm

    • Therefore, the rise in the water level is 7.39 cm.
    • Therefore the correct option is b)7.39.
    General
    Maths-

    The circumference of the base of a 12 cm high wooden solid cone is 44 cm. Find the volume

    Hint:- Volume of a cone = (1 third)πr2h
    Circumference of base = 2πr
    Solution :- We have given the dimensions of a wooden solid cone
    Circumference = 44 m = 2πr
    44 = 2 (22 over 7) r
    r = (44 x 7) / 44
    r = 7
    Radius, r = 7 m
    Height, h = 12 m
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1/3)πr2h
    = (1 third)(3.14)(7 x 7)(12)
    = (1 third)(3.14) (49 x 12)
    = (1 third)(3.14)(588)
    = 1848 / 3
    = 616 cm3
    Therefore, the volume of wooden cone is 616 cm3
    Therefore correct option is a) 616 cm3.

    The circumference of the base of a 12 cm high wooden solid cone is 44 cm. Find the volume

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Circumference of base = 2πr
    Solution :- We have given the dimensions of a wooden solid cone
    Circumference = 44 m = 2πr
    44 = 2 (22 over 7) r
    r = (44 x 7) / 44
    r = 7
    Radius, r = 7 m
    Height, h = 12 m
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1/3)πr2h
    = (1 third)(3.14)(7 x 7)(12)
    = (1 third)(3.14) (49 x 12)
    = (1 third)(3.14)(588)
    = 1848 / 3
    = 616 cm3
    Therefore, the volume of wooden cone is 616 cm3
    Therefore correct option is a) 616 cm3.
    parallel
    General
    Maths-

    Given length, breadth, and height of a cuboid are 15 cm, 37.5 cm, and 48 cm. Find the cube edge whose given volume is equal to the volume of this cuboid. Also, calculate the length of the diagonal to the nearest natural number.

    We are given the dimensions of the cuboid
    Length = l = 15cm
    Breadth = b =37.5cm
    Height = h = 48cm
    Volume of a cuboid = l × b × h =
    = 15 × 37.5 × 48
    = 27000 cm3
    As from the given condition ,
    Volume of cube = volume of cuboid
    a3 = 27000
    a = cube root of 27000
    a = 30
    Therefore the length of diagonal = left parenthesis square root of 3 right parenthesisa
    = left parenthesis square root of 3 right parenthesis 30
    = (1.734 )30
    = 51.9
    = 52
    Therefore, the correct answer is d) 30cm , 52cm

    Given length, breadth, and height of a cuboid are 15 cm, 37.5 cm, and 48 cm. Find the cube edge whose given volume is equal to the volume of this cuboid. Also, calculate the length of the diagonal to the nearest natural number.

    Maths-General
    We are given the dimensions of the cuboid
    Length = l = 15cm
    Breadth = b =37.5cm
    Height = h = 48cm
    Volume of a cuboid = l × b × h =
    = 15 × 37.5 × 48
    = 27000 cm3
    As from the given condition ,
    Volume of cube = volume of cuboid
    a3 = 27000
    a = cube root of 27000
    a = 30
    Therefore the length of diagonal = left parenthesis square root of 3 right parenthesisa
    = left parenthesis square root of 3 right parenthesis 30
    = (1.734 )30
    = 51.9
    = 52
    Therefore, the correct answer is d) 30cm , 52cm
    General
    Maths-

    Vtotal = Vcone 1+Vcone 2 Find the volume of the composite solid.
    Use 3.14 for pi.

    We have given the dimensions of a Cones in the given figure
    For Cone 1
    Radius, r = 6 cm
    Height, h = 7 cm
    For Cone 2
    Radius, R = 10 cm
    Height, H = 6 cm
    We have to find the volume of the given cone
    We know that
    Volume of a Cone 1 = (1 third)πr2h
    = (1 third)(3.14)(6 x 6)(7)
    = (1 third)(3.14) (36 x 7)
    = (1 third)(3.14)(252)
    = 791.28 / 3
    = 263.76 cm3
    Volume of a Cone 1 = (1 third)πR2H
    = (1 third)(3.14)(10 x 10)(6)
    = (1 third)(3.14) (100 x 6)
    = (1 third)(3.14)(600)
    = 1884 over 3
    = 628 cm3
    We know that Vtotal=Vcone 1+Vcone 2
    Vtotal = 263.76 + 628 = 891.76 cm3
    Therefore, the total volume of the composite solid is 891.76 cm3
    Therefore correct option is a)891.76 cm3 .

    Vtotal = Vcone 1+Vcone 2 Find the volume of the composite solid.
    Use 3.14 for pi.

    Maths-General
    We have given the dimensions of a Cones in the given figure
    For Cone 1
    Radius, r = 6 cm
    Height, h = 7 cm
    For Cone 2
    Radius, R = 10 cm
    Height, H = 6 cm
    We have to find the volume of the given cone
    We know that
    Volume of a Cone 1 = (1 third)πr2h
    = (1 third)(3.14)(6 x 6)(7)
    = (1 third)(3.14) (36 x 7)
    = (1 third)(3.14)(252)
    = 791.28 / 3
    = 263.76 cm3
    Volume of a Cone 1 = (1 third)πR2H
    = (1 third)(3.14)(10 x 10)(6)
    = (1 third)(3.14) (100 x 6)
    = (1 third)(3.14)(600)
    = 1884 over 3
    = 628 cm3
    We know that Vtotal=Vcone 1+Vcone 2
    Vtotal = 263.76 + 628 = 891.76 cm3
    Therefore, the total volume of the composite solid is 891.76 cm3
    Therefore correct option is a)891.76 cm3 .
    General
    Maths-

    Given edges of the cubes as 3 cm, 4 cm, and 5 cm respectively. Its now melted and made into one single cube. Calculate the edge of a new cube.

    Let the cubes be A, B and C and their sides are x, y and z respectively
    x= 3cm
    y=4cm
    z= 5cm
    And let the side if final cube is w
    We will first add the volumes of the three cubes A, B and C
    Vol(A) + Vol(B) + Vol(C) = x3 + y3 + z3
    = 33 + 43 + 53
    = 27 + 64 + 125
    = 216
    The sum of volumes of cubes A , B and C is equal to the resultant cube we obtain by melting these three,
    Volume of final cube =  Vol(A) + Vol(B) + Vol(C)
    (w)3 = 216
    We know that 216 is the cube of 6
    Therefore, w = 6
    Therefore, the correct option is b) 6 .

    Given edges of the cubes as 3 cm, 4 cm, and 5 cm respectively. Its now melted and made into one single cube. Calculate the edge of a new cube.

    Maths-General
    Let the cubes be A, B and C and their sides are x, y and z respectively
    x= 3cm
    y=4cm
    z= 5cm
    And let the side if final cube is w
    We will first add the volumes of the three cubes A, B and C
    Vol(A) + Vol(B) + Vol(C) = x3 + y3 + z3
    = 33 + 43 + 53
    = 27 + 64 + 125
    = 216
    The sum of volumes of cubes A , B and C is equal to the resultant cube we obtain by melting these three,
    Volume of final cube =  Vol(A) + Vol(B) + Vol(C)
    (w)3 = 216
    We know that 216 is the cube of 6
    Therefore, w = 6
    Therefore, the correct option is b) 6 .
    parallel
    General
    Maths-

    Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a large plastic cup of Mike in shape of cone
    Radius, r = 3 in
    Height, h = 7 in
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1 third)πr2h
    = (1 third)(3.14)(3 x 3)(7)
    = (1 third)(3.14) (9 x 7)
    = (1 third)(3.14)(63)
    = 197.82 over 3
    = 65.94 in3
    = 66 in3
    Therefore, the volume of Mike’s cup is 66 in3
    Therefore correct option is c) 66 in3.

    Mike has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mike’s cup?

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a large plastic cup of Mike in shape of cone
    Radius, r = 3 in
    Height, h = 7 in
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1 third)πr2h
    = (1 third)(3.14)(3 x 3)(7)
    = (1 third)(3.14) (9 x 7)
    = (1 third)(3.14)(63)
    = 197.82 over 3
    = 65.94 in3
    = 66 in3
    Therefore, the volume of Mike’s cup is 66 in3
    Therefore correct option is c) 66 in3.
    General
    Maths-

    The dimensions of a cubical box are in the ratio of 5:4:3.and the length of the diagonal is 10√2. Calculate the total surface area?

    We have given that, dimensions of cubical box are in the ratio of 5:4:3.
    Let the dimensions of the box are

    Length = 5x

    Breadth= 4x

    Height = 3x
    We have given diagonal , therefore we can write,
    square root of open parentheses l squared plus b squared plus h squared close parentheses end root equals 10 square root of 2
    Lets put the assumed values of length , breadth and height in the above equation,
    square root of left parenthesis 5 x right parenthesis squared plus left parenthesis 4 x right parenthesis squared plus left parenthesis 3 x right parenthesis squared end root equals 10 square root of 2
    square root of 25 x squared plus 16 straight x squared plus 9 straight x squared end root equals 10 square root of 2
    square root of 50 x squared end root equals 10 square root of 2
    We can write as square root of 50 x squared end root text  as  end text 5 square root of 2 x,
    5 square root of 2 x equals 10 square root of 2
    Divide both sides of equation by 5 square root of 2
    x = 2
    Therefore, the dimensions of cuboid are,
    Length = 5x = 5(2)= 10

    Breadth= 4x = 4(2) =8

    Height = 3x=3(2)= 6

    • Putting the values in the formula of surface area

    Area = 2[(10)(8) + (8)(6) + (6)(10)]

    = 2[80 + 48 + 60]

    = 2(188)

    Area =376
    Therefore, the correct option is b)376.

    The dimensions of a cubical box are in the ratio of 5:4:3.and the length of the diagonal is 10√2. Calculate the total surface area?

    Maths-General
    We have given that, dimensions of cubical box are in the ratio of 5:4:3.
    Let the dimensions of the box are

    Length = 5x

    Breadth= 4x

    Height = 3x
    We have given diagonal , therefore we can write,
    square root of open parentheses l squared plus b squared plus h squared close parentheses end root equals 10 square root of 2
    Lets put the assumed values of length , breadth and height in the above equation,
    square root of left parenthesis 5 x right parenthesis squared plus left parenthesis 4 x right parenthesis squared plus left parenthesis 3 x right parenthesis squared end root equals 10 square root of 2
    square root of 25 x squared plus 16 straight x squared plus 9 straight x squared end root equals 10 square root of 2
    square root of 50 x squared end root equals 10 square root of 2
    We can write as square root of 50 x squared end root text  as  end text 5 square root of 2 x,
    5 square root of 2 x equals 10 square root of 2
    Divide both sides of equation by 5 square root of 2
    x = 2
    Therefore, the dimensions of cuboid are,
    Length = 5x = 5(2)= 10

    Breadth= 4x = 4(2) =8

    Height = 3x=3(2)= 6

    • Putting the values in the formula of surface area

    Area = 2[(10)(8) + (8)(6) + (6)(10)]

    = 2[80 + 48 + 60]

    = 2(188)

    Area =376
    Therefore, the correct option is b)376.

    General
    Maths-

    Calculate the amount of ice cream this cone can hold (just to the top of the cone). Round to the nearest hundredth.

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a ice cream cone
    Diameter = 4.5 cm
    Radius , r = 4.5 over 2 = 2.25 cm
    Height , h = 11 cm
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1/3)πr2h
    = (1 third)(3.14)(2.25 x 2.25)(11)
    = (1 third)(3.14) (5.06 x 11)
    = (1 third)(3.14)(55.68)
    = 174.85 over 3
    = 58.29 cm3
    Therefore, the volume of ice cream cone is 58.29 cm3
    Therefore correct option is a)58.29 cm3.

    Calculate the amount of ice cream this cone can hold (just to the top of the cone). Round to the nearest hundredth.

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a ice cream cone
    Diameter = 4.5 cm
    Radius , r = 4.5 over 2 = 2.25 cm
    Height , h = 11 cm
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1/3)πr2h
    = (1 third)(3.14)(2.25 x 2.25)(11)
    = (1 third)(3.14) (5.06 x 11)
    = (1 third)(3.14)(55.68)
    = 174.85 over 3
    = 58.29 cm3
    Therefore, the volume of ice cream cone is 58.29 cm3
    Therefore correct option is a)58.29 cm3.
    parallel
    General
    Maths-

    Given dimensions of the room are 24 cm in breadth, 30 cm in height and 18 cm in length. Find the length of the longest pole that can be placed in the room

    We have given the dimensions of room
    Length l =18 cm
    Breadth b = 24cm
    Height h = 30cm
    To find the length of the longest pole that can be placed in the room
    We have formula = square root of open parentheses l squared plus b squared plus h squared close parentheses end root
    square root of 18 squared plus 24 squared plus 30 squared end root
    square root of 324 plus 576 plus 900 end root
    square root of 1800
    30 square root of 2
    = 42.426 cm

    Given dimensions of the room are 24 cm in breadth, 30 cm in height and 18 cm in length. Find the length of the longest pole that can be placed in the room

    Maths-General
    We have given the dimensions of room
    Length l =18 cm
    Breadth b = 24cm
    Height h = 30cm
    To find the length of the longest pole that can be placed in the room
    We have formula = square root of open parentheses l squared plus b squared plus h squared close parentheses end root
    square root of 18 squared plus 24 squared plus 30 squared end root
    square root of 324 plus 576 plus 900 end root
    square root of 1800
    30 square root of 2
    = 42.426 cm
    General
    Maths-

    Mr. Quintero has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mr. Quintero's cup r = 3, h = 7

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a large plastic cup of Mr. Quintero in shape of cone
    Radius, r = 3 in
    Height, h = 7 in
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1 third)πr2h
    = (1 third)(3.14)(3 x 3)(7)
    = (1 third)(3.14) (9 x 7)
    = (1 third)(3.14)(63)
    = 197.82 over 3
    = 65.94 in3
    = 66 in3
    Therefore, the volume of Mr. Quintero’s cup is 66 in3
    Therefore correct option is c) 66 in3.

    Mr. Quintero has a large plastic cup that he is going to fill with water. The plastic cup is in the shape of a cone as shown. Which is closest to the volume of Mr. Quintero's cup r = 3, h = 7

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a large plastic cup of Mr. Quintero in shape of cone
    Radius, r = 3 in
    Height, h = 7 in
    We have to find the volume of the given cone
    We know that
    Volume of a cup = (1 third)πr2h
    = (1 third)(3.14)(3 x 3)(7)
    = (1 third)(3.14) (9 x 7)
    = (1 third)(3.14)(63)
    = 197.82 over 3
    = 65.94 in3
    = 66 in3
    Therefore, the volume of Mr. Quintero’s cup is 66 in3
    Therefore correct option is c) 66 in3.
    General
    Maths-

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

    • 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.

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

    Maths-General
    • 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.
    parallel
    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

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