Volume and Surface Area problems
- 1. If each side of a cube is decreased by 19%, then decrease in surface area is?
Options- A. 40%
- B. 38.4%
- C. 35%
- D. 34.39% Discuss
Correct Answer: 34.39%
Explanation:
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 %
- 2. If the side of a cube is increased by 12%, by how much per cent does its volume increase?
Options- A. 40.4928%
- B. 50.5240%
- C. 60.3292%
- D. 30.4928% Discuss
Correct Answer: 40.4928%
Explanation:
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%
- 3. Find the volume of a right circular cylinder of length 80 cm and diameter of the base 14 cm.?
Options- A. 1400 cm3
- B. 1553 cm3
- C. 12320 cm3
- D. 13320 cm3 Discuss
Correct Answer: 12320 cm3
Explanation:
Given, r = 7 cm, h = 80 cm
Volume = ?r2h = (22/7) x 7 x 7 x 80
= 12320 cm3
- 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.?
Options- A. 2068 sq cm
- B. 1825 sq cm
- C. 1925 sq cm
- D. 2160 sq cm Discuss
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
- 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. (? = 3.14)?
Options- A. 5 cm
- B. 8 cm
- C. 3 cm
- D. 4 cm Discuss
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
- 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?
Options- A. 2/10 cm
- B. 2/?10 cm
- C. 1/?10 cm
- D. 1/10 cm Discuss
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.
- 7. 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
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
- 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?
Options- A. 6020 sq cm
- B. 5052 sq cm
- C. 7045 sq cm
- D. 7040 sq cm Discuss
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
- 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?
Options- A. 4 : 9
- B. 9 : 4
- C. 20 : 27
- D. 27 : 20 Discuss
Correct Answer: 20 : 27
Explanation:
Let 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
- 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?
Options- A. 7 : 3
- B. 3 : 7
- C. 7 : 6
- D. 6 : 7 Discuss
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
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