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Quiz: Volume and Surface Area

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Number of Questions: 19

Question: 11 -

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted to form a solid cylinder of base diameter 8 cm. What is the height of the cylinder?

Options:

  1. 4.57

  2. 4.7

  3. 4.67

  4. 4.5

    5. Answer:

    4.67
    Solution:

    Let the height of the cylinder be h.
    According to question:
    Volume of cylinder = Volume of hollow sphere
    Apti Volume and Surface Area

Question: 12 -

A 6 m long and 4 m wide cistern contains water up to a breadth of 1 m 25 cm. Find the total surface area of the surface immersed in water?

Options:

  1. 49

  2. 64

  3. 52

  4. 42 

    5. Answer:

    49
    Solution:

    Area of the wet surface =
    2[lb+ bh+ hl] - lb = 2 [bh+ lh] + lb
    = 2[(4*1.25+6*1.25)] +6*4 = 49 m2

    Solution 2:
    The area of the wet surface= Area of the base + area of the two walls 2 * (4 *1.25) + area of the other two walls 2 * (6 * 1.25) cm
    = 6*4 + 2 (4*1.25) + 2 (6*1.25)
    = 24+ 10 + 15 = 49 m2

Question: 13 -

The length, breadth, and height of a brick are 10 cm, 4 cm, and 3 cm, respectively. Find the surface area of the brick?

Options:

  1. 156 

  2. 164 

  3. 160 

  4. 154 

    5. Answer:

    164 
    Solution:

    Surface area of a Cuboid = 2(lb+ bh+ hl) cm2
    So,
    Surface area of a brick = 2(10*4+4*3+3*10) cm2
    = 2(82) cm2= 164 cm2

Question: 14 -

A copper sphere of radius 3 cm is beaten and drawn into a wire of diameter 0.2 cm. The length of the wire is

Options:

  1. 36

  2. 21

  3. 18

  4. 9

    5. Answer:

    36
    Solution:

    Radius of wire =Apti Volume and Surface Area = 0.1

    Volume of sphere = Volume of cylinder
    Apti Volume and Surface Area

Question: 15 -

The radius of road roller is 1 meter and length 7/22 meter. When it is rolled on a ground then it rolls 500 times to level the ground. But it was found that on 5% part of the ground, roller rolled twice. What is the total area of the ground?

Options:

  1. 950 

  2. 975 

  3. 975 sqrt(Π) m2

  4. 1000/Π2 m2

    5. Answer:

    950 
    Solution:

    Let the area of the ground = x meter
    The area covered in 1 revolution by the roller = 2Πrl
    Apti Volume and Surface Area