Discussion
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- Question
- 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?
Options- A. 4 : 9
- B. 9 : 4
- C. 20 : 27
- D. 27 : 20
- Correct Answer
- 20 : 27
ExplanationLet radii be 2r and 3r and heights be 5h and 3h.
? Ratio of volumes = [?(2r)2 x 5h] / [?(3r)2 x 3h]
= 20/27 = 20 : 27 - 1. What will be the curved surface area of a right circular cylinder having length 160 cm and radius of the base is 7 cm?
Options- A. 6020 sq cm
- B. 5052 sq cm
- C. 7045 sq cm
- D. 7040 sq cm Discuss
- 2. What is the height of a solid cylinder of radius 5 cm and total surface area is 660 sq cm?
Options- A. 10 cm
- B. 12 cm
- C. 15 cm
- D. 16 cm Discuss
- 3. 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?
Options- A. 2/10 cm
- B. 2/?10 cm
- C. 1/?10 cm
- D. 1/10 cm Discuss
- 4. 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. (? = 3.14)?
Options- A. 5 cm
- B. 8 cm
- C. 3 cm
- D. 4 cm Discuss
- 5. 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.?
Options- A. 2068 sq cm
- B. 1825 sq cm
- C. 1925 sq cm
- D. 2160 sq cm Discuss
- 6. 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?
Options- A. 7 : 3
- B. 3 : 7
- C. 7 : 6
- D. 6 : 7 Discuss
- 7. 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
- 8. 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
- 9. 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
- 10. 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
Volume and Surface Area problems
Search Results
Correct Answer: 7040 sq cm
Explanation:
Curved surface area of the cylinder = 2?rh
= 2 x (22/7) x 7 x 160
= 7040 sq cm
Correct Answer: 16 cm
Explanation:
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
? 2?rh + 2?r2 = 660
? 2?r(h + r) = 660
? (h + 5) = 330/5? = 330/5 x 7/22
? h = 66 x (7/22) - 5 = 21 - 5
? Required height = 16 cm
Correct Answer: 2/?10 cm
Explanation:
Given, r1 = 1 cm, h1 = 30 cm, h2 = 300 cm.
Volume of rod = Volume of wire
? ?r12h1 = ?r22h2
? ? x (1)2 x 30 = ? x r22 x 300
? r22 = 30/300
? r2 = 1/?10 cm
? diameter = 2r2
= 2 x 1/?10 = 2/?10cm.
Correct Answer: 3 cm
Explanation:
Given, lateral surface area = 94.2 sq cm
? 2?rh = 94.2
? r = 94.2/(2?h) = 94.2/(2 x 3.14 x 5) = 3 cm
Correct Answer: 2068 sq cm
Explanation:
Total surface area of cylinder = 2?r(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
Correct Answer: 7 : 3
Explanation:
Given that , 2?rh = 264
and ?r2h = 924
? ( ?r2h) / (2?rh) = 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
Correct Answer: 8%
Explanation:
According to the formula,
Percentage change in volume is directly proportional to the height,
So percentage decrease in volume = 8%
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%
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)
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
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