Problems on Volume and Surface Area

Problems on Volume and Surface Area

Learn and practice Problems on volume and surface area with easy explaination and shortcut tricks. All questions and answers on volume and surface area covered for various Competitive Exams

Solve Problems:

1) The surface area of a cube is 600 cm2. The length of its diagonal is

  1. 5 cm
  2. 15 cm
  3. 10 root 3  cm
  4. 10  cm
View Answer

Answer: C

Explanation:

Surface area of cube = 6 a2
600 = 6 a2
a2 = 100
                                                    a= =10 cm
Diagonal of cube = a = × 10 = 10 cm

2) The length of the longest rod that can be placed in a room 30 m long, 24 m broad and 18 m high, is

  1. 30 m
  2. 15  m
  3. 30  m
  4. 60 m
View Answer

Answer: C

Explanation:

Length of room = 30 m
Breadth of room = 24 m
Height of room = 18 m

3) 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.

  1. 150
  2. 140
  3. 120
  4. 100
View Answer

Answer: D

Explanation:

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 =

4) 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

  1. 48 cm2
  2. 40 cm2
  3. 36 cm2
  4. 32 cm2
View Answer

Answer: A

Explanation:

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

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5) 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?

  1. Rs. 6000
  2. Rs. 8000
  3. Rs. 9000
  4. Rs. 10,000
View Answer

Answer: A

Explanation:

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

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

  1. 1500 m3
  2. 1400 m3
  3. 1200 m3
  4. 1000 m3
View Answer

Answer: A

Explanation:

1 hectare = 10,000 m2
1.5 hectare = 1.5 x 10 x 1000 = 15,000 m2
Depth = 10 cm of rainfall =10/100

∴ Volume of water = Area * Depth
15,000 *10/100 = 1500 m3

7) 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.

  1. 14,400 cm2
  2. 44,200 cm2
  3. 57,600 cm2
  4. 86,400 cm2
View Answer

Answer: D

Explanation:

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
Surface area of cube = 6 a2
= 6 x 1202= 86,400 cm2

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

  1. 30808 cm3
  2. 38808 cm3
  3. 380808 cm3
  4. 380800 cm3
View Answer

Answer: B

Explanation:

Surface area of sphere = 4 π r2=5544 cm2

Volume of a sphere

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

  1. 8 : 27
  2. 4 : 9
  3. 6 : 12
  4. 1 : 15
View Answer

Answer: A

Explanation:

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

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

  1. 1: 3
  2. 2: 1
  3. 1: 1
  4. 2: 3
View Answer

Answer: D

Explanation:

Radius of hemisphere = 3 cm

Ratio = 2: 3

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