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Quiz: Volume and Surface Area

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Number of Questions: 19

Question: 6 -

The radius of hemisphere is 3 cm. The ratio of its volume to the total surface area is

Options:

  1. 1: 1

  2. 2: 3

  3. 1: 3

  4. 2: 1

    5. Answer:

    2: 3
    Solution:

    Radius of hemisphere = 3 cm
    Apti Volume and Surface Area Apti Volume and Surface Area
    Ratio = 2: 3

Question: 7 -

If two spheres have their radii in the ratio 2: 3, the ratio of their volumes is

Options:

  1. 6 : 12

  2. 8 : 27

  3. 1 : 15

  4. 4 : 9

    5. Answer:

    8 : 27
    Solution:

    Let the radius of both the spheres be 'r' and 'R', respectively.
                     r: R = 2: 3
    Volume of sphere = Apti Volume and Surface Area
    Ratio between the volume of spheres =Apti Volume and Surface Area
                                       =8:27

Question: 8 -

Surface area of a sphere is 5544 cm2. Its volume will be

Options:

  1. 380808 

  2. 30808 

  3. 38808 

  4. 380800 

    5. Answer:

    38808 
    Solution:

    Surface area of sphere = 4 π r2=5544 cm2
    Apti Volume and Surface Area
    Volume of a sphere Apti Volume and Surface Area

Question: 9 -

The radii of two cylinders are in the ratio of 2: 3 and their heights are in the ratio of 5: 3. The ratio of their volume is

Options:

  1. 20: 27

  2. 4: 9

  3. 20: 25

  4. 9: 4

    5. Answer:

    20: 27
    Solution:

    Let the radius of both cylinders be 2x and 3x.
    Let the height of both cylinders be 5y and 3y.
    Ratio of the volume of two cylinders Apti Volume and Surface Area
    Ratio = 20: 27

Question: 10 -

If the curved surface area of a sphere is same as the curved surface area of a hemisphere, find the radius of the hemisphere.

Options:

  1. 2 times that of the sphere

  2. sqrt(2) times that of the sphere

  3. sqrt(3) times that of the sphere

  4. Same as that of the sphere

    5. Answer:

    sqrt(2) times that of the sphere
    Solution:

    Curved surface area of a sphere = Curved surface area of a hemisphere
                  4 π R2= 2 π r2
                     2 R2= r2
    Radius of hemisphere i.e. 'r' = Apti Volume and Surface Area= Apti Volume and Surface Area R