Volume and Surface Area problems
- 1. The height of cylinder is 14 cm and its curved surface area is 264 sq. cm. The volume of the cylinder is?
Options- A. 308 cm3
- B. 396 cm3
- C. 1448 cm3
- D. 1232 cm3 Discuss
Correct Answer: 396 cm3
Explanation:
? 2?rh = 264
? 2 x (22/7) x r x 14 = 264
? r = 3
So, Volume = ?r2h
= (22/7) x 3 x 3 x 14 cm3
= 396 cm3
- 2. The percentage increased in the surface area of a cube when each side is doubled, is?
Options- A. 25%
- B. 50%
- C. 150%
- D. 300% Discuss
Correct Answer: 300%
Explanation:
Original area = 6a2
New area = 6(2a)2 = 24a2
Required increased % = (18a2/6a2) x 100%
= 300%
- 3. If the radius of a sphere is doubled, then its surface area is increased by?
Options- A. 100%
- B. 200%
- C. 300%
- D. 50% Discuss
Correct Answer: 300%
Explanation:
Original area = 4? r2,
New area = 4?(2r)2 = 16 ? r2
Required increased % = [12?r2]/[4? r2] x 100 %= 300%
- 4. If the height of a come is doubled, then its volume is increased by?
Options- A. 100%
- B. 200%
- C. 300%
- D. 400% Also asked in: AIEEE, Bank Exams, CAT, GATE, GRE, Bank Clerk, Bank PO
Correct Answer: 100%
Explanation:
Original volume = 1/3 ?r2h;
New volume = 1/3 ?r2(2h) = 2/3?r2h
Required increased % = [?r2h/3]/[?r2h/3] x 100%
= 100%
- 5. If the radius of a sphere is doubled, then its volume is increased by?
Options- A. 100 %
- B. 200 %
- C. 700 %
- D. 800 % Discuss
Correct Answer: 700 %
Explanation:
Original volume = 4/3?r3
New volume = 4/3 ? (2r)3 = 32/3 ?r3
Required increased % = [(28/3) ?r3] x [(3/4)?r3] x 100 % = 700 %
- 6. The radius of two cylinders are in the ratio of 2 : 3 and their height are in the ratio 5 : 3 . The ratio of their volumes is?
Options- A. 27 : 20
- B. 20 : 27
- C. 4 : 9
- D. 9 : 4 Discuss
Correct Answer: 20 : 27
Explanation:
Let their radii be 2r and 3r and height 5h and 3h respectively.
? Ratio of their volumes = [?(2r)2 x 5h] / [?(3r)2 x 3h]
= 20/27 = 20 : 27
- 7. Two circular cylinders of equals volume have their heights in the ratio 1 : 2 Ratio of their radii is?
Options- A. 1 : ?2
- B. ?2 : 1
- C. 1 : 2
- D. 1 : 4 Discuss
Correct Answer: ?2 : 1
Explanation:
Let their height be h and 2h radii be x and y respectively.
Then, ?x2h = ?y2(2h)
? x2/y2 = 2/1
? x/y = ?2 / 1 = ?2 : 1
- 8. The radii of two spheres are in the ratio 1 : 2 . The ratio of their surface areas is?
Options- A. 1 : 2
- B. 1 : 4
- C. 1 : ?2
- D. 3 : 8 Discuss
Correct Answer: 1 : 4
Explanation:
Let their radii be x and 2x .
Ratio of their surface areas = [4?x2]/[4?(2x)2] = 1/4 = 1 : 4
- 9. A radius of the base of a right circular cone is 6 cm and its slant height is 28 cm. The curved surface area of the cone is?
Options- A. 268 sq. cm
- B. 528 sq. cm
- C. 462 sq. cm
- D. 658 sq. cm Discuss
Correct Answer: 528 sq. cm
Explanation:
Curved surface area = ?rl
= (22/7 x 6 x 28) cm2
= 528 cm2
- 10. How many bullets can be made out of a cube of lead whose edge measures 22 cm, each bullet being 2 cm in diameter?
Options- A. 5324
- B. 2662
- C. 1347
- D. 2541 Discuss
Correct Answer: 2541
Explanation:
Number of bullets = Volume of cube / Volume of 1 bullet
= (22 x 22 x 22)/(4/3 x 22/7 x 1 x 1 x 1)
= 2541.
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