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Quiz: Volume and Surface Area

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Number of Questions: 19

Question: 1 -

The dimensions of a piece of iron in the shape of a cuboid are 270 cm x 100 cm x 64 cm. If it is melted and recast into a cube, find the surface of the cube.

Options:

  1. 44,200

  2. 57,600

  3. 14,400

  4. 86,400

    5. Answer:

    86,400
    Solution:

    Volume of iron piece = l x b x h
                                       = 270 x 100 x 64 = 1,728,000 cm3
    Volume of cuboid = volume of cube
                1,728,000 = a3
                   a Apti Volume and Surface Area
    Surface area of cube = 6 a2
    = 6 x 1202= 86,400 cm2

Question: 2 -

A water tank is 30 m long, 20 m wide and 12 m deep. It is made of iron sheet which is 3 m wide. The tank is open at the top. If the cost of iron sheet is Rs. 10 per meter, what is the total cost of iron sheet required to build the tank?

Options:

  1. Rs. 9000

  2. Rs. 10,000

  3. Rs. 6000

  4. Rs. 8000

    5. Answer:

    Rs. 6000
    Solution:

    Length of water tank = 30 m
    Width of water tank = 20 m
    Depth of water tank = 12 m

    Area of water tank = 2(lb+bh +hl) - lb

                                             = 2 (30 x 20 + 20 x 12 + 12 x 30) - 30 x 20
                                            = 2 (600 + 240 + 360) - 600
                                             = 2 (1200) - 600
                                             = 2400 - 600 = 1800 m2

    Area of iron sheet (L*B) = area of tank = 1800 m2

                              L * B = 1800
                              L x 3 = 1800
                              L = 1800/3 = 600 m

    Given that, the cost of iron sheet is Rs. 10 per meter.
    So, the total cost of iron sheet to build the tank = 10 x 600 = Rs. 6000

Question: 3 -

4 cubes each of 6 cm2 total surface area and another cube of 24 cm2 total surface area are placed together in such a way to form a rectangular parallelepiped. The total surface area of the parallelepiped so formed is

Options:

  1. 40 

  2. 32 

  3. 48 

  4. 36 

    5. Answer:

    48 
    Solution:

    Total surface area of parallelepiped = total surface area of 4 cubes + Surface area of another cube
    So, the required surface area = 4 x6 + 24 = 48 cm2

Question: 4 -

In a shower 10 cm of rain falls. What is the volume of water that falls on 1.5 hectares of ground?

Options:

  1. 1200 

  2. 1500 

  3. 1000 

  4. 1400 

    5. Answer:

    1500 
    Solution:

    1 hectare = 10,000 m2
    1.5 hectare = 1.5 x 10 x 1000 = 15,000 m2
    Depth = 10 cm of rainfall =Apti Volume and Surface Area

    ∴ Volume of water = Area * Depth
    15,000 *Apti Volume and Surface Area = 1500 m3

Question: 5 -

The dimensions of a hall are 40 m, 25 m and 20 m. If each person requires 200 cubic meters, find the number of persons who can be accommodated in the hall.

Options:

  1. 140

  2. 150

  3. 120

  4. 100

    5. Answer:

    100
    Solution:

    Length of the hall = 40 m
    Breadth of hall= 25 m
    Height of hall = 20 m
    Volume of the hall = l x b x h
                               = 40 x 25 x 20 = 20,000 m3
    Space occupied by each person = 200m3
    Number of person that can accommodate in the hall =Apti Volume and Surface Area