Discussion
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- Question
- 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
- Correct Answer
- 8000
ExplanationNumber 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 - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. A cylindrical piece of metal of radius 2 cm and height 6 cm is shaped into a cone of same radius. The height of the cone is?
Options- A. 18 cm
- B. 14 cm
- C. 12 cm
- D. 8 cm Discuss
- 9. If the volumes of two cones are in ratio 1 : 4 and their diameter are in the ratio 4 : 5, then the ratio of their heights is?
Options- A. 1 : 5
- B. 5 : 4
- C. 5 : 16
- D. 25 : 64 Discuss
- 10. If a right circular cone of vertical height 24 cm has a volume of 1232 cm 3, then the area of its curved surface is?
Options- A. 1254 cm2
- B. 704 cm2
- C. 550 cm2
- D. 154 cm2 Discuss
Volume and Surface Area problems
Search Results
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: 528 sq. cm
Explanation:
Curved surface area = ?rl
= (22/7 x 6 x 28) cm2
= 528 cm2
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
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: 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
Correct Answer: 18 cm
Explanation:
? 1/3 ? x (2)2 x h = ? x (2)2 x 6
? h = 18 cm
Correct Answer: 25 : 64
Explanation:
Since the diameters are in the ratio 4 : 5. It follows that their radii are in the ratio 4 : 5.
Let them be 4r and 5r. Let the height be h and H .
? Ratio of volumes = [(1/3)?(4r)2h / (1/3)?(5r)2H
= (16h)/(25H)
? h/H = (1/4) x (25/16) = 25/64 = 25: 64.
Correct Answer: 550 cm2
Explanation:
? 1/3 x (22/7) x r2 x 24 = 1232
? r2 = 1232 x (7/22) x (3/24) = 49
? r = 7 cm
Now, h = 24
So, l = ?72 + (24)2
= ?625
= 25 cm
? Curved surface area = ?rl
= (22/7) x 7 x 25 cm2
= 550 cm2
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