Question 1

If each side of a cube is decreased by 19%, then decrease in surface area is?

Accepted Answer

Here, x = y = -19% According to the formula, Percentage decrease in surface area = [x + y + xy/100]% = [- 19 - 19 + (-19) x (-19) /100]% =[-38 + 361/100]% = [-38 + 3.61]% = -34.39 %

Question 2

If the side of a cube is increased by 12%, by how much per cent does its volume increase?

Accepted Answer

Here, k = 12% According to the formula, Percentage increase in volume = [(1 + k/100)3 - 1] x 100% = [(1 + 12/100)3 - 1] x 100% = [(1.12)3 - 1] x 100% = 0.404928 x 100% = 40.4928%

Question 3

Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.?

Accepted Answer

Given, r = 7 cm, h = 80 cm Volume = πr2h = (22/7) x 7 x 7 x 80 = 12320 cm3

Question 4

The diameter of the base of a right circular cylinder is 14 cm, while its length is 40 cm. Find the total surface area of the cylinder.?

Accepted Answer

Total surface area of cylinder = 2πr(h + r) Given that, r = 14/2 = 7 cm, h = 40 cm ∴ Required total surface area = 2 x (22/7) x 7 x (40 + 7) = 44 x 47 = 2068 sq cm

Question 5

If the lateral surface area of a cylinder is 94.2 sq cm and its height is 5 cm, then find the radius of its base. (π = 3.14)?

Accepted Answer

Given, lateral surface area = 94.2 sq cm ⇒ 2πrh = 94.2 ∴ r = 94.2/(2πh) = 94.2/(2 x 3.14 x 5) = 3 cm

Question 6

A rod of 2 cm diameter and 30 cm length is converted into a wire of 3 cm length of uniform thickness. The diameter of the wire is?

Accepted Answer

Given, r1 = 1 cm, h1 = 30 cm, h2 = 300 cm. Volume of rod = Volume of wire ⇒ πr12h1 = πr22h2 ⇒ π x (1)2 x 30 = π x r22 x 300 ⇒ r22 = 30/300 ∴ r2 = 1/√10 cm ∴ diameter = 2r2 = 2 x 1/√10 = 2/√10cm.

Question 7

What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq cm?

Accepted Answer

Let the height and radius and radius of solid cylinder be h and r cm respectively Given that, radius (r) = 5 cm and total surface area = 660 cm2 ⇒ 2πrh + 2πr2 = 660 ⇒ 2πr(h + r) = 660 ⇒ (h + 5) = 330/5π = 330/5 x 7/22 ⇒ h = 66 x (7/22) - 5 = 21 - 5 ∴ Required height = 16 cm

Question 8

What will be the curved surface area of a right circular cylinder having length 160 cm and radius of the base is 7 cm?

Accepted Answer

Curved surface area of the cylinder = 2πrh = 2 x (22/7) x 7 x 160 = 7040 sq cm

Question 9

The ratio of the radii of two cylinders is 2 : 3 and the ratio of their heights is 5 : 3 . The ratio of their volumes will be?

Accepted Answer

Let radii be 2r and 3r and heights be 5h and 3h. ∴ Ratio of volumes = [π(2r)2 x 5h] / [π(3r)2 x 3h] = 20/27 = 20 : 27

Question 10

The curved surface area of a cylindrical pillar is 264 sq m and its volume is 924 m 3. The ratio of its diameter to its height is?

Accepted Answer

Given that , 2πrh = 264 and πr2h = 924 ∴ ( πr2h) / (2πrh) = 924 / 264 = 7/2 ⇒ r/2 = 7/2 ⇒ r = 7 ∴ d = 2r = 14 m Also, 2 x (22/7) x 7 x h = 264 ⇒ h = 264 / 44 = 6 ∴ d/h = 14/6 = 7/3 = 7 : 3

Question 11

If height of cylinder is decreased by 8%, while its radius remains unchanged, by what per cent does the volume decrease?

Accepted Answer

According to the formula, Percentage change in volume is directly proportional to the height, So percentage decrease in volume = 8%

Question 12

If the radius of a cylinder is increased by 25% and its height remains unchanged, then find the percent increase in volume.?

Accepted Answer

According to the formula Percentage increase in volume = (2k + k2/100)% = ( 2 x 25 + 252/100)% = (50 + 625/100)% = (50 + 6.25)% = 56.25%

Question 13

If the radius of a cylinder is decreased by 8%, while its height is increased by 4%, what will be the effect on volume?

Accepted Answer

Here, A = -8%, B = 4% According to the formula, Net effect on volume = [2A + B + A2 + 2AB/100 + A2B/1002]% = [2 x (-8) + 4 + (-8)2 + 2 x (-8) x 4 /100 + (-8)2 x 4 /1002] = [-16 + 4 + 64 - 64/100 + 256/104]% =[-12 + 0 + 0.0256]% = -11.9744% (decrease)

Question 14

The floor of a rectangular hall has a perimeter 250 m. If the cost of painting the four walls at the rate of ₹ 10 per sq m is ₹15000, then find the height of the hall?

Accepted Answer

Area of 4 wails = Lateral surface area perimeter = 2(l + b) = 250 ⇒ l + b = 250/2 = 125 m Area to be painted = Cost/Rate = 15000/10 = 1500 sq m Area of 4 wails = 2(l + b)h = 250 h ⇒ 250h = 1500 ∴ h = 1500/250 = 6 m

Question 15

The diameter of a roller is 84 cm and its length 120 cm. Its takes 500 complete revolutions to move once over to level a playground (in sq m)?

Accepted Answer

In one revolution, area covered = Covered surface area ⇒ 2πrh = 2 x (22/7) x 42 x 120 = 31680 sq cm in 500 revolutions, Area covered = 31680 x 500 = (1584 x 104) sq cm = (1584 x 104) / (104) = 1584 sq m

Question 16

A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the covered surface of the pillar at the rate ₹ 10 per sq m .?

Accepted Answer

Curved surface area = 2πrh = 2 x (22/7) x 0.25 x 3.5 = 5.5 sq m ∴ Cost of painting 5.5 sq m = 10 x 5.5 = ₹ 55

Question 17

A pillar 14 cm in diameters is 5 m high. How much material was used to construct it?

Accepted Answer

Volume of the cylinder = πr2h = (22/7) x 7 x 7 x 500 = 77000 = (77 x 103) cm3

Question 18

The curved surface area of a right circular cone of radius 14 cm is 440 sq cm. what is the slant height of the cone?

Accepted Answer

Curved surface area of right circular cone = πrl ∴ 440 = (22/7) x 14 x l ⇒ l = (440 x 7) / (22 x 14) = 10 cm

Question 19

The diameter if base of a right circular cone is 7 cm and height is 10 cm , then what is its lateral surface area?

Accepted Answer

Given that, Diameter of a right circular cone = 7 cm ∴ Radius of a right circular cone = 7/2 cm and slant height of a right circular cone (l) = 10 cm ∴ Lateral surface area of a cone = πrl = (22/7) x (7/2) x 10 = 11 x 10 = 110 cm2

Question 20

What is volume of a cone having a base of radius 10 cm and height 21 cm?

Accepted Answer

Volume of cone = (1/3)πr2h = (1/3) x (22/7) x 10 x 10 x 21 = 2200 cm3

Volume and Surface Area Questions