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- Question
- 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
- Correct Answer
- 1 : 4
ExplanationLet their radii be x and 2x .
Ratio of their surface areas = [4?x2]/[4?(2x)2] = 1/4 = 1 : 4 - 1. 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
- 2. 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
- 3. If the radius of a sphere is doubled, then its volume is increased by?
Options- A. 100 %
- B. 200 %
- C. 700 %
- D. 800 % Discuss
- 4. If the height of a come is doubled, then its volume is increased by?
Options- A. 100%
- B. 200%
- C. 300%
- D. 400% Discuss
- 5. 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
- 6. 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
- 7. 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
- 8. A spherical lead ball of radius 10 cm is melted and small lead balls of radius 5 mm are made. The total number of possible small lead balls.?
Options- A. 800
- B. 125
- C. 400
- D. 8000 Discuss
- 9. A come of height 7 cm and base radius 3 cm is curved from a rectangular block of wood 10 cm x 5 cm x 2 cm. The percentage of wood wasted is?
Options- A. 34%
- B. 46%
- C. 54%
- D. 66% Discuss
- 10. The material of a cone is converted into the shape of a cylinder of equal radius . If the height of the cylinder is 5 cm. the height of the cone is?
Options- A. 10 cm
- B. 15 cm
- C. 18 cm
- D. 24 cm Discuss
Volume and Surface Area problems
Search Results
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
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
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 %
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%
Correct Answer: 300%
Explanation:
Original area = 4? r2,
New area = 4?(2r)2 = 16 ? r2
Required increased % = [12?r2]/[4? r2] x 100 %= 300%
Correct Answer: 528 sq. cm
Explanation:
Curved surface area = ?rl
= (22/7 x 6 x 28) cm2
= 528 cm2
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.
Correct Answer: 8000
Explanation:
Number of balls = Volume of big ball / Volume of 1 small ball
= [4/3 x ? x 10 x 10 x 10] / [4/3 x ? x 0.5 x 0.5 x 0.5]
= 8000
Correct Answer: 34%
Explanation:
Total volume of cuboid = (10 x 5 x 2) cm3
= 100 cm3
Volume curved = 1/3 x (22/7) x 3 x 3 x 7 cm3
= 66 cm3
% of wood wasted = (100 - 66)% = 34 %
Correct Answer: 15 cm
Explanation:
? (1/3)?r2 x h = ?r2 x 5
? h = 15 cm
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