Question 1

A cistern 6m long and 4 m wide contains water up to a depth of 1 m 25 cm. The total area of the wet surface is:

Accepted Answer

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

Question 2

A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

Accepted Answer

Volume of water displaced = (3 x 2 x 0.01) m3 = 0.06 m3. ∴ Mass of man = Volume of water displaced x Density of water = (0.06 x 1000) kg = 60 kg.

Question 3

How many bricks, each measuring 25 cm x 11.25 cm x 6 cm, will be needed to build a wall of 8 m x 6 m x 22.5 cm?

Accepted Answer

Number of bricks = Volume of the wall = ❨ 800 x 600 x 22.5 ❩ = 6400. Volume of 1 brick 25 x 11.25 x 6

Question 4

A right triangle with sides 3 cm, 4 cm and 5 cm is rotated the side of 3 cm to form a cone. The volume of the cone so formed is:

Accepted Answer

Clearly, we have r = 3 cm and h = 4 cm. ∴ Volume = 1 Πr2h = ❨ 1 x Π x 32 x 4 ❩cm3 = 12Π cm3. 3 3

Question 5

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the ratio of its diameter to its height.

Accepted Answer

Πr2h = 924 ⟹ r = ❨ 924 x 2 ❩ = 7 m. 2Πrh 264 264 And, 2Πrh = 264 ⟹ h = ❨ 264 x 7 x 1 x 1 ❩ = 6m. 22 2 7 ∴ Required ratio = 2r = 14 = 7 : 3. h 6

Question 6

What is the total surface area of a right circular cone of height 14 cm and base radius 7 cm?

Accepted Answer

h = 14 cm, r = 7 cm. So, l = √(7)2 + (14)2 = √245 = 7√5 cm. ∴ Total surface area = Πrl + Πr2 = ❨ 22 x 7 x 7√5 + 22 x 7 x 7 ❩cm2 7 7 = [154(√5 + 1)] cm2 = (154 x 3.236) cm2 = 498.35 cm2.

Question 7

50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 m3, then the rise in the water level in the tank will be:

Accepted Answer

Total volume of water displaced = (4 x 50) m 3 = 200 m 3 . ∴ Rise in water level = ❨ 200 ❩m 0.25 m = 25 cm. 40 x 20

Question 8

66 cubic centimetres of silver is drawn into a wire 1 mm in diameter. The length of the wire in metres will be:

Accepted Answer

Let the length of the wire be h Radius = 1 mm = 1 cm. Then, 2 20 ⟹ 22 x 1 x 1 x h = 66. 7 20 20 ⟹ h = ❨ 66 x 20 x 20 x 7 ❩ = 8400 cm = 84 m. 22

Question 9

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of the areas of four walls, the volume of the hall is:

Accepted Answer

2(15 + 12) x h = 2(15 x 12) ⟹ h = 180 m = 20 m. 27 3 ∴ Volume = ❨ 15 x 12 x 20 ❩m3 = 1200 m3. 3

Question 10

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

Accepted Answer

Let the thickness of the bottom be x cm. Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000 ⟹ 320 x 250 x (110 - x) = 8000 x 1000 ⟹ (110 - x) = 8000 x 1000 = 100 320 x 250 ⟹ x = 10 cm = 1 dm.

Question 11

A large cube is formed from the material obtained by melting three smaller cubes of 3, 4 and 5 cm side. What is the ratio of the total surface areas of the smaller cubes and the large cube?

Accepted Answer

Volume of the large cube = (3 3 + 4 3 + 5 3 ) = 216 cm 3 Let the edge of the large cube be a. So, a3 = 216 ⟹ a = 6 cm. ∴ Required ratio = ❨ 6 x (32 + 42 + 52) ❩ = 50 = 25 : 18. 6 x 62 36

Question 12

A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs 8 g/cm3, then the weight of the pipe is:

Accepted Answer

External radius = 4 cm, Internal radius = 3 cm. Volume of iron = ❨ 22 x [(4)2 - (3)2] x 21 ❩cm3 7 = ❨ 22 x 7 x 1 x 21 ❩cm3 7 = 462 cm3. ∴ Weight of iron = (462 x 8) gm = 3696 gm = 3.696 kg.

Question 13

In a shower, 5 cm of rain falls. The volume of water that falls on 1.5 hectares of ground is:

Accepted Answer

1 hectare = 10,000 m 2 So, Area = (1.5 x 10000) m2 = 15000 m2. Depth = 5 m = 1 m. 100 20 ∴ Volume = (Area x Depth) = ❨ 15000 x 1 ❩m3 = 750 m3. 20

Question 14

A metallic sheet is of rectangular shape with dimensions 48 m x 36 m. From each of its corners, a square is cut off so as to make an open box. If the length of the square is 8 m, the volume of the box (in m3) is:

Accepted Answer

Clearly, l = (48 - 16)m = 32 m, b = (36 -16)m = 20 m, h = 8 m. ∴ Volume of the box = (32 x 20 x 8) m3 = 5120 m3.

Question 15

The slant height of a right circular cone is 10 m and its height is 8 m. Find the area of its curved surface.

Accepted Answer

l = 10 m, h = 8 m. So, r = √l2 - h2 = √(10)2 - 82 = 6 m. ∴ Curved surface area = Πrl = (Π x 6 x 10) m2 = 60Π m2.

Question 16

The volume of a cube is 512 cm 3, Its surface area is?

Accepted Answer

∵ a3 = 512 = 8 x 8 x 8 ⇒ a = 8 cm ∵ Surface area = 6a2 =[6 x (8)2] cm2 =384 cm2

Question 17

The surface area of a cube is 726 m 2. Its volume is?

Accepted Answer

Surface area = 6a2 = 726 ⇒ a2 = 121 ⇒ a = 11 cm ∴ Volume of the cube = (11 x 11 x 11) cm3 = 1331 cm3

Question 18

If each side of a cube is doubled, then its volume? .

Accepted Answer

Let the edge of original cube = x cm Edge of new cube = (2x) cm Ratio of their volumes = x3 : (2x)3 = x3 : 8x3 = 1 :8 Thus the volumes be comes 8 times.

Question 19

Three metal cubes of sides 5 cm, 4 cm and 3 cm are melted and recast into a new cube. The length of the edge of this cube, is?

Accepted Answer

Volume of new cube = (5)3 + (4)3 + (3)3 cm3 = 126 cm3 Edge of this cube = (6 x 6 x 6)1/3 = 6 cm

Question 20

If the volumes of two cubes are in the ratio 8 : 1, the ratio of their edges, is?

Accepted Answer

Volume of new cube = [(5)3 + (4)3 + (3)3] cm3 = 216 cm3 Edge of this cube = ( 6 x 6 x 6)1/3 = 6 cm

Volume and Surface Area Questions