Maths-
General
Easy

Question

What is the length of the longest pole that can be fit in the room of dimensions 5m x 10m x 5m

  1. 12.25
  2. 11.95
  3. 12.85
  4. 11.85

Hint:

 Diagonal of cubesquare root of 3 × side = square root of 3a unit

The correct answer is: 12.25


    The dimensions of the room are
    Length = 5m
    Breadth = 10m
    Height = 5m
    We know that
    Length of the longest pole = length of diagonal = square root of open parentheses l squared plus b squared plus h squared close parentheses end root
    By substituting the values
    Length of the longest pole = square root of open parentheses 5 squared plus 10 squared plus 5 squared close parentheses end root
    So we get
    Length of the longest pole = square root of blank end root left parenthesis 25 plus 100 plus 25 right parenthesis
    By addition
    Length of the longest pole = square root of 150 equals 12.25 straight m
    Therefore, the length of the longest pole that can be put in the room is 12.25m.
    The correct option is a)12.25.

    Related Questions to study

    General
    Maths-

    The square on the diagonal of a cube has an area of 192 cm2. Find the T.S.A of the cube.

    Given:         Side of the cube = s
    Length of diagonal on one face of cube = l
    Length of diagonal of the cube = z
    We know that,
    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 l equals s square root of 2 end cell row cell z equals s square root of 3 end cell end table
    Given z²=192 cm²
    Squaring the equation of Z on both sides we get,

    z squared equals left parenthesis s square root of 3 right parenthesis squared
    192 = s²×3
    s² =192/3

    s2 = 64

    s = 8 cm
    Total surface area of cube = 6s²
    TSA = 6×8² = 6×64 = 384 cm²
    Hence side of given cube = S = 8 cm
    and Total surface area of cube =TSA= 384 cm²

    Therefore, the correct option is d) 384.

    The square on the diagonal of a cube has an area of 192 cm2. Find the T.S.A of the cube.

    Maths-General
    Given:         Side of the cube = s
    Length of diagonal on one face of cube = l
    Length of diagonal of the cube = z
    We know that,
    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 l equals s square root of 2 end cell row cell z equals s square root of 3 end cell end table
    Given z²=192 cm²
    Squaring the equation of Z on both sides we get,

    z squared equals left parenthesis s square root of 3 right parenthesis squared
    192 = s²×3
    s² =192/3

    s2 = 64

    s = 8 cm
    Total surface area of cube = 6s²
    TSA = 6×8² = 6×64 = 384 cm²
    Hence side of given cube = S = 8 cm
    and Total surface area of cube =TSA= 384 cm²

    Therefore, the correct option is d) 384.

    General
    Maths-

    Two adjacent sides of the right-angle pf a right-angled triangle are 3 cm and 4 cm. This triangle is revolved around the side of length 3 cm. Find the volume of the cone thus formed. Find also the slant height of the cone (π =3.14).

    We have given the dimensions of triangle having sides adjacent to the right angles equal to 3 cm, 4cm
    Therefore by pythagorous theorem third side (slant height) will be
    equals square root of 3 squared plus 4 squared end root equals square root of 9 plus 16 end root equals square root of 25 equals 5
    It is revolved about 3 cm side
    Therefore, the cone formed will have dimensions as
    Height, h = 3 cm
    Radius, r = 4 cm
    So, the volume of cone = (1/3)πr2h
    = (1/3)(22/7)(4 x 4)(3)
    = 22/7 x 16
    = 352 / 7
    = 50.28 cm3
    Therefore, the correct option is c) 5 cm

    Two adjacent sides of the right-angle pf a right-angled triangle are 3 cm and 4 cm. This triangle is revolved around the side of length 3 cm. Find the volume of the cone thus formed. Find also the slant height of the cone (π =3.14).

    Maths-General
    We have given the dimensions of triangle having sides adjacent to the right angles equal to 3 cm, 4cm
    Therefore by pythagorous theorem third side (slant height) will be
    equals square root of 3 squared plus 4 squared end root equals square root of 9 plus 16 end root equals square root of 25 equals 5
    It is revolved about 3 cm side
    Therefore, the cone formed will have dimensions as
    Height, h = 3 cm
    Radius, r = 4 cm
    So, the volume of cone = (1/3)πr2h
    = (1/3)(22/7)(4 x 4)(3)
    = 22/7 x 16
    = 352 / 7
    = 50.28 cm3
    Therefore, the correct option is c) 5 cm
    General
    Maths-

    Write the factored form of the given expression.
    49 x squared minus 25

    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:- (7x - 4) (7x + 4) is the factorized form of the given expression.
    Explanation :-
    Given, 49 x squared minus 25
    Write 25 text  as  end text left parenthesis 5 right parenthesis squared text  and  end text 49 x squared text  as  end text left parenthesis 7 x right parenthesis squared text  we get  end text open parentheses left parenthesis 7 x right parenthesis squared minus left parenthesis 5 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 ,49 x squared minus 25 equals left parenthesis 7 x minus 5 right parenthesis left parenthesis 7 x plus 5 right parenthesis
    ∴  (7x - 5)(7x + 5) is the factorized form of the given expression.

    Write the factored form of the given expression.
    49 x squared minus 25

    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:- (7x - 4) (7x + 4) is the factorized form of the given expression.
    Explanation :-
    Given, 49 x squared minus 25
    Write 25 text  as  end text left parenthesis 5 right parenthesis squared text  and  end text 49 x squared text  as  end text left parenthesis 7 x right parenthesis squared text  we get  end text open parentheses left parenthesis 7 x right parenthesis squared minus left parenthesis 5 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 ,49 x squared minus 25 equals left parenthesis 7 x minus 5 right parenthesis left parenthesis 7 x plus 5 right parenthesis
    ∴  (7x - 5)(7x + 5) is the factorized form of the given expression.
    parallel
    General
    Maths-

    The volume of a cone is 7.8 cm3 and the area of its base is 3.9 cm2, find its height?

    We have given the values of
    Volume of cone = 7.8 cm3
    Area of its base = 3.9 cm2
    We have to find the height of cone
    We know that
    Volume of a cone = (1/3)πr2h
    Area of base = πr2
    Let us divide both these formulas to get the value of height
    fraction numerator text  Volume of a cone  end text over denominator text  Area of base  end text end fraction equals fraction numerator 1 third pi r squared h over denominator pi r squared end fraction
    fraction numerator 7.8 over denominator 3.9 end fraction equals h over 3
    h equals fraction numerator 7.8 cross times 3 over denominator 3.9 end fraction
    h equals fraction numerator 23.4 over denominator 3.9 end fraction
    h = 6
    Therefore, the height of the given cone is 6 cm
    Therefore, the correct option is d) 6 cm

    The volume of a cone is 7.8 cm3 and the area of its base is 3.9 cm2, find its height?

    Maths-General
    We have given the values of
    Volume of cone = 7.8 cm3
    Area of its base = 3.9 cm2
    We have to find the height of cone
    We know that
    Volume of a cone = (1/3)πr2h
    Area of base = πr2
    Let us divide both these formulas to get the value of height
    fraction numerator text  Volume of a cone  end text over denominator text  Area of base  end text end fraction equals fraction numerator 1 third pi r squared h over denominator pi r squared end fraction
    fraction numerator 7.8 over denominator 3.9 end fraction equals h over 3
    h equals fraction numerator 7.8 cross times 3 over denominator 3.9 end fraction
    h equals fraction numerator 23.4 over denominator 3.9 end fraction
    h = 6
    Therefore, the height of the given cone is 6 cm
    Therefore, the correct option is d) 6 cm
    General
    Maths-

    Dimensions of the cuboid are in the ratio of 5 : 4: 2 and the whole surface area is 684 cm2, find the volume of the cuboid?

    We are given that

    Length, breadth and height of a cuboid are in the ratio 5:4:2 and the total surface area is 684 cm2,

    Let, the dimension of cuboid are

    l = 5x,

    b = 4x

    and h = 2x

    Now,

    Surface area of cuboid = 2((5x cross times4x) + (4xcross times2x) + (2xcross times5x))

    = 2((20x2)+(8x2)+(10x2))

    = 2(38 x2)

    = 76x2

    Surface area of cuboid = 684

    76x= 684

    x= 9

    Now,

    x = 3

    Dimensions of cuboid are,

    l = 5x = 5cross times3 =15cm,

    b = 4x = 4cross times3 = 12cm

    h = 2x = 2cross times3 = 6cm

    Volume of cuboid = l cross timescross times h

    = 15 cross times 12 cross times 6

    = 1080 cm3

    Hence, the volume of cuboid is 1080 cm3 is the answer.

    Therefore , the correct option is a)1080

    Dimensions of the cuboid are in the ratio of 5 : 4: 2 and the whole surface area is 684 cm2, find the volume of the cuboid?

    Maths-General
    We are given that

    Length, breadth and height of a cuboid are in the ratio 5:4:2 and the total surface area is 684 cm2,

    Let, the dimension of cuboid are

    l = 5x,

    b = 4x

    and h = 2x

    Now,

    Surface area of cuboid = 2((5x cross times4x) + (4xcross times2x) + (2xcross times5x))

    = 2((20x2)+(8x2)+(10x2))

    = 2(38 x2)

    = 76x2

    Surface area of cuboid = 684

    76x= 684

    x= 9

    Now,

    x = 3

    Dimensions of cuboid are,

    l = 5x = 5cross times3 =15cm,

    b = 4x = 4cross times3 = 12cm

    h = 2x = 2cross times3 = 6cm

    Volume of cuboid = l cross timescross times h

    = 15 cross times 12 cross times 6

    = 1080 cm3

    Hence, the volume of cuboid is 1080 cm3 is the answer.

    Therefore , the correct option is a)1080

    General
    Maths-

    Radius and slant height of a cone are 20 cm and 29 cm respectively. Find its volume

    Hint:- Volume of a cone = (1/3)πr2h
    By applying Pythagoras theorem  on the cone, we can find the relation between volume and slant height of the cone.
    We know, h2 + r2 = L2
    h equals square root of open parentheses L squared minus r squared close parentheses end root
    where,
    • h is the height of the cone,
    • r is the radius of the base, and,
    • L is the slant height of the cone.
    The volume of the cone in terms of slant height can be given as
    V equals left parenthesis 1 divided by 3 right parenthesis pi r squared h equals left parenthesis 1 divided by 3 right parenthesis pi r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    Solution:- We have given that
    Radius, r = 20 cm
    Slant height , L = 29 cm
    Therefore, volume of cone = left parenthesis 1 divided by 3 with _ below right parenthesis m r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    = (1/3)(3.14)(20 x 20) left parenthesis 1 divided by 3 with _ below right parenthesis straight capital pi r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    = (1/3)(3.14)(400) √(841 - 400)
    = (1/3)(1256) √(441)
    = (1/3)(1256)(21)
    = 1256 x 7
    = 8792 cm3
    Therefore, the volume of given cone is 8792 cm3
    Therefore option c) 8792 cm3 is correct.

    Radius and slant height of a cone are 20 cm and 29 cm respectively. Find its volume

    Maths-General
    Hint:- Volume of a cone = (1/3)πr2h
    By applying Pythagoras theorem  on the cone, we can find the relation between volume and slant height of the cone.
    We know, h2 + r2 = L2
    h equals square root of open parentheses L squared minus r squared close parentheses end root
    where,
    • h is the height of the cone,
    • r is the radius of the base, and,
    • L is the slant height of the cone.
    The volume of the cone in terms of slant height can be given as
    V equals left parenthesis 1 divided by 3 right parenthesis pi r squared h equals left parenthesis 1 divided by 3 right parenthesis pi r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    Solution:- We have given that
    Radius, r = 20 cm
    Slant height , L = 29 cm
    Therefore, volume of cone = left parenthesis 1 divided by 3 with _ below right parenthesis m r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    = (1/3)(3.14)(20 x 20) left parenthesis 1 divided by 3 with _ below right parenthesis straight capital pi r squared square root of blank end root open parentheses L squared minus r squared close parentheses
    = (1/3)(3.14)(400) √(841 - 400)
    = (1/3)(1256) √(441)
    = (1/3)(1256)(21)
    = 1256 x 7
    = 8792 cm3
    Therefore, the volume of given cone is 8792 cm3
    Therefore option c) 8792 cm3 is correct.
    parallel
    General
    Maths-

    The area of a base of a cuboid is 48 cm2 and its height and length of the diagonal are 3 cm and 13 cm respectively. Calculate the length and width of the box?

    Let a be the length and b be the width and c be height of rectangular solid whose area of the base will be (ab) m2 and

    length of diagonal = square root of a squared plus b squared plus c squared end root

    So accordingly

    (a)(b)=48 ……………..(1) and

    square root of a squared plus b squared plus c squared end root equals 13. text  or.  end text a squared plus b squared plus c squared equals 169

    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 plus b squared equals 169 minus c squared end cell row cell a squared plus b squared equals 169 minus 9 end cell end table

    a2+b2=160-------------(2).

    Now using formula. (a + b)= a2+b2+2.ab

    (a + b)= 160 + 2 × 48

    (a + b)= 160 + 96 = 256

    Taking square root of both sides

    or. a + b = 16……………(3)

    and. (a - b)= a+ b- 2.ab

    ( a- b)= 160 – 96 = 64

    Taking square root of both sides

    or. a - b = 8…………………(4). ,

    By adding eqn. (3) and (4) we get,

    2a = 24.

    a = 24/2 = 12 m.

    Putting a = 12 in eqn. (3)

    12 + b = 16

    b = 16 – 12

    b = 4 m.

    Thus , length =12 m , width = 4 m.

    Therefore, the correct option is c)12cm , 4cm.

    The area of a base of a cuboid is 48 cm2 and its height and length of the diagonal are 3 cm and 13 cm respectively. Calculate the length and width of the box?

    Maths-General
    Let a be the length and b be the width and c be height of rectangular solid whose area of the base will be (ab) m2 and

    length of diagonal = square root of a squared plus b squared plus c squared end root

    So accordingly

    (a)(b)=48 ……………..(1) and

    square root of a squared plus b squared plus c squared end root equals 13. text  or.  end text a squared plus b squared plus c squared equals 169

    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 plus b squared equals 169 minus c squared end cell row cell a squared plus b squared equals 169 minus 9 end cell end table

    a2+b2=160-------------(2).

    Now using formula. (a + b)= a2+b2+2.ab

    (a + b)= 160 + 2 × 48

    (a + b)= 160 + 96 = 256

    Taking square root of both sides

    or. a + b = 16……………(3)

    and. (a - b)= a+ b- 2.ab

    ( a- b)= 160 – 96 = 64

    Taking square root of both sides

    or. a - b = 8…………………(4). ,

    By adding eqn. (3) and (4) we get,

    2a = 24.

    a = 24/2 = 12 m.

    Putting a = 12 in eqn. (3)

    12 + b = 16

    b = 16 – 12

    b = 4 m.

    Thus , length =12 m , width = 4 m.

    Therefore, the correct option is c)12cm , 4cm.

    General
    Maths-

    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

    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.

    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

    Maths-General
    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.

    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.

    parallel
    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.
    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
    parallel
    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 .
    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.
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.