Question 1

A hemisphere has 28 cm diameter. Find its curved surface area.?

Accepted Answer

Curved surface area = 2πr2 = 2π x 14 x 14 = 2 x (22/7) x 14 x 14 = 2 x 22 x 2 x 14 = 88 x 14 = 1232 sq cm

Question 2

What will be the difference between total surface area and curved surface area of a hemisphere having 2 cm diameter?

Accepted Answer

Given, Diameter = 2 cm ∴ r = 1 cm Now, Total surface area of hemisphere = 3πr2 and curved surface area = 2πr2 Required difference = 3πr2 - 2πr2 = πr2 = π x 12 = π sq cm

Question 3

A metallic sphere of radius 12 cm is melted into three smaller spheres. If the radii of two smaller spheres are 6 cm and 8 cm, the radius of the third is?

Accepted Answer

Let radius of the third sphere be r. Then, 4/3 π x (12)3 = 4/3 π x (6)3 + 4/3π x (8)3 + 4/3 πr3 ⇒ (12)3 = (6)3 + (8)3 + r3 ⇒ r3 = 1728 - 216 - 512 ⇒ r3 = 1000 ∴ r = 10 cm

Question 4

If the radius of a sphere is increased by 3%, then what percent increase takes place in surface area of the sphere?

Accepted Answer

According to the formula Percentage increase in surface area = [ 2x + x2/100]% = [2 x 3 + (3)2/100]% = [6 + 0.09]% = 6.09%

Question 5

If radius of a sphere is decreased by 24%, by what per cent does its surface area decrease?

Accepted Answer

According to the formula, Percentage decrease in surface area = [2 x (-24) + (-24) x (-24)/100]% = [-48 + 5.76]% = - 42.24%

Question 6

If the radius of a sphere is increased by 100%, by what per cent does its volume increase?

Accepted Answer

Here, n = 100% According to the formula Percentage increase in volume = [(1 + n/100)3 - 1] x 100% = [(1 + 100/100)3 - 1] x 100% = [8 - 1] x 100% = 700%

Question 7

Weight of a solid metallic sphere of radius 4 cm is 4 kg. The weight of a hollow sphere made with same metal, whose outer diameter is 16 cm and inner diameter is 12 cm, is?

Accepted Answer

Volume of solid sphere of radius 4 cm = (4/3)π(4)3 cm3 Volume of hollow sphere = 4/3π[(8)3 - (6)3] cm3 ∵ Weight of 4/3π(4)3 cm3 = 4 kg = 4(512 - 216)/43 = 18.5 kg

Question 8

A prism has the base a right angled triangle whose sides adjacent to the right angle are 10 cm and 12 cm long. The height of the prism is 20 cm. The density of the material of the prism is 6 g/cu cm. The weight of the prism is?

Accepted Answer

Volume of prism = Area of base x Height = (1/2) x 10 x 12 x 20 = 1200 cm2 ∴ Weight of prism = 1200 x 6 = 7200 g = 7.2 kg

Question 9

The perimeter of the triangular base of a right prism is 60 cm and the sides of the base are in the ratio 5 : 12 : 13. Then, its volume will be (height of the prism being 60 cm).?

Accepted Answer

Let the sides of the base are 5k, 12k and 13k, respectively. Given, perimeter of base = 60 cm ⇒ 5k + 12k + 13k = 60 ∴ k = 60/30 = 2 The sides of base are 10 cm, 24 cm 26 cm. ∴ Volume of prism = (1/2) x 10 x 24 x 50 = 6000 cm3

Question 10

A prism and a pyramid have the same base and the same height. Find the ratio of the volumes of the prism and the pyramid?

Accepted Answer

Volume of the prism = (Area of the base ) x (Height) Volume of the pyramid = 1/3 (Area of the base ) x (Height) Required ratio = [A x H] / [(1/3) x A x H] Therefore, Ratio of the volumes of the prism and the pyramid = 3 : 1.

Question 11

The base of a cone and a cylinder have the same radius 6 cm. They have also the same height 8 cm. The ratio of the curved surface of the cylinder to that of the cone is?

Accepted Answer

Ratio of curved surface area of cylinder and cone = [2πrh] / [πr√h2 + r2] = [2 x 6 x 8] / [6 x √62 + 82] = 96/(6 x 10) = 96/60 = 8/5 = 8 : 5

Question 12

A solid metallic cylinder of base radius 3 cm and height 5 cm is melted to form cones, each of height 1 cm and base radius 1 mm. The number of cones is?

Accepted Answer

Let required number of coins be n, Then, n x 1/3 x π (1/10)2 x 1 = π x (3)2 x 5 ∴ n = 9 x 5 x 3 x 100 = 13500

Question 13

How many spherical bullets can be made out of a solid cube whose edge measures 44 cm, each bullet being 4 cm in diameter?

Accepted Answer

Volume of 1 bullet = 4/3π(2)3 = (32/3 x 22/7) cm3 Volume of the cube = (44)3 ∴ Number of bullets = Volume of solid/Volume of 1 bullet = (44)3 x 3 x 7 / 32 x 22 = 2541

Question 14

The volumes of a sphere and a right circular cylinder having the same radius are equal. The ratio of the diameter of the sphere to the height of the cylinder is?

Accepted Answer

Let r = Radius of cylinder = Radius of sphere, h = Height of the cylinder. According to the question. 4/3πr3 = πr2h ⇒ h = 4r/3 ⇒ 4r = 3h ⇒ 2r = 3/2h ⇒ 2r/h = 3/2 ∴ Required ration = 3 : 2

Question 15

The radius of a sphere and a right circular cylinder are equal and their curved surface areas are also equal. The ratio of their volumes is?

Accepted Answer

Given, 4πr2 = 2πrh ∴ h = 2r Now, required ratio = 4/3πr3 : πr2h = 4r : 3h = 4r : 6r [ ∴ h = 2r] = 2 : 3

Question 16

The volume of a cuboid is twice the volume of a cube. If the dimensions of total cuboid are 9 cm, 8 cm and 6 cm, then total surface area of the cube will be?

Accepted Answer

Volume of the cuboid = 9 x 8 x 6 = 432 cm3 Volume of the cube = 1/2 x 432 = 216 cm3 ∴ Each side of cube = ∛216 = 6 cm Total surface area of the cube = 6 x (Side)2 = 6 x 62 = 6 x 36 = 216 sq cm

Question 17

Seven equal cubes each of side 5 cm are joined end-to-end. Find the surface area of the resulting cuboid .?

Accepted Answer

Given, l = Length of the cuboid = 5 x 7 = 35 cm h = Breadth of the cuboid = 5 cm h = Height of the cuboid = 5 cm ∴ Surface area = 2(lb + bh + lh) = 2[35 x 5 + 5 x 5 + 35 x 5] = 2[175 + 25 + 175] = 2 x 375 = 750 sq cm

Question 18

In a shower, 10 cm of rain falls, What will be the volume of water that falls on 1 hect area of ground?

Accepted Answer

1 hec = 10000 m3 Volume of water = Base area x Height = (10000 x 10)/100 = 1000 m3

Question 19

Water flows at the rate of 10 m/min from a cylindrical pipe 5 mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth is 24 cm?

Accepted Answer

Given, radius of pipe 5/2 x 10 = 5/20 cm [∵ 1 cm = 10 mm] Height of pipe = 1000 cm Radius of vessel = 20 cm and height = 24 cm Volume of water flow in one minute from cylindrical pipe = π (5/20)2 x 1000 = 125/2 π cm3 and volume of conical vessel = 1/3 π(20)2 x 24 = 3200π cm3 ∴ Required time = (3200π x 2) / 125π = 511/5 or 51 min 12 s

Question 20

A cylindrical jar, whose base has a radius of 15 cm, is filled with water upto a height of 20 cm, A solid iron spherical ball of radius 10 cm is dropped in the jar to submerge completely in water. Find the increase in the level of water (in cm).?

Accepted Answer

Let level of water will be increased by h cm π x (15)2 x h = (4/3)π(10)3 ∴ h = [(4/3) x 10 x 10 x 10] / [15 x 15] = 525/27 cm

Volume and Surface Area Questions