Volume and Surface Area problems
- 1. If height of cylinder is decreased by 8%, while its radius remains unchanged, by what per cent does the volume decrease?
Options- A. 4%
- B. 6%
- C. 8%
- D. 10% Discuss
Correct Answer: 8%
Explanation:
According to the formula,
Percentage change in volume is directly proportional to the height,
So percentage decrease in volume = 8%
- 2. If the radius of a cylinder is increased by 25% and its height remains unchanged, then find the percent increase in volume.?
Options- A. 56.25%
- B. 52.25%
- C. 50.4%
- D. 60.26% Discuss
Correct Answer: 56.25%
Explanation:
According to the formula
Percentage increase in volume
= (2k + k2/100)% = ( 2 x 25 + 252/100)%
= (50 + 625/100)% = (50 + 6.25)%
= 56.25%
- 3. If the radius of a cylinder is decreased by 8%, while its height is increased by 4%, what will be the effect on volume?
Options- A. 11.9744% (decrease)
- B. 11.9744% (increase)
- C. 12.4678% (decrease)
- D. 12.4678% (increase) Discuss
Correct Answer: 11.9744% (decrease)
Explanation:
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)
- 4. 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?
Options- A. 8 m
- B. 6 m
- C. 9 m
- D. 7 m Discuss
Correct Answer: 6 m
Explanation:
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
- 5. 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)?
Options- A. 1632
- B. 1817
- C. 1532
- D. 1584 Discuss
Correct Answer: 1584
Explanation:
In one revolution, area covered = Covered surface area
? 2?rh = 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
- 6. 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 .?
Options- A. ? 50
- B. ? 68
- C. ? 98
- D. ? 55 Discuss
Correct Answer: ? 55
Explanation:
Curved surface area = 2?rh
= 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
- 7. A pillar 14 cm in diameters is 5 m high. How much material was used to construct it?
Options- A. (77 x 102)cm3
- B. (77 x 104)cm3
- C. (77 x 105)cm3
- D. (77 x 103)cm3 Discuss
Correct Answer: (77 x 103)cm3
Explanation:
Volume of the cylinder = ?r2h
= (22/7) x 7 x 7 x 500 = 77000
= (77 x 103) cm3
- 8. 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?
Options- A. 10 cm
- B. 11 cm
- C. 12 cm
- D. 13 cm Discuss
Correct Answer: 10 cm
Explanation:
Curved surface area of right circular cone = ?rl
? 440 = (22/7) x 14 x l
? l = (440 x 7) / (22 x 14) = 10 cm
- 9. The diameter if base of a right circular cone is 7 cm and height is 10 cm , then what is its lateral surface area?
Options- A. 110 sq cm
- B. 100 sq cm
- C. 70 sq cm
- D. 49 sq cm Discuss
Correct Answer: 110 sq cm
Explanation:
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 = ?rl = (22/7) x (7/2) x 10
= 11 x 10 = 110 cm2
- 10. What is volume of a cone having a base of radius 10 cm and height 21 cm?
Options- A. 2200 cm3
- B. 3000 cm3
- C. 5600 cm3
- D. 6600 cm3 Discuss
Correct Answer: 2200 cm3
Explanation:
Volume of cone = (1/3)?r2h
= (1/3) x (22/7) x 10 x 10 x 21 = 2200 cm3
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