Volume and Surface Area problems
- 1. 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
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
- 2. 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
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 %
- 3. 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
Correct Answer: 15 cm
Explanation:
? (1/3)?r2 x h = ?r2 x 5
? h = 15 cm
- 4. 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
Correct Answer: 18 cm
Explanation:
? 1/3 ? x (2)2 x h = ? x (2)2 x 6
? h = 18 cm
- 5. 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
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.
- 6. 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
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
- 7. A cylindrical vessel 60 cm in diameter is partially filled with water. A sphere 60 cm in diameter is gently dropped into the vessel. To what further height will water rise in the cylinder?
Options- A. 15 cm
- B. 30 cm
- C. 40 cm
- D. 25 cm Discuss
Correct Answer: 40 cm
Explanation:
Let h and H be the height of water level before and after the dropping of the sphere.
Then, [? x (30)2 x H ] - [? x (30)2 x h ]
= 4/3 ? x (30)3
? ? x 900 x (H -h) = 4/3 ? x 27000
? (H- h) = 40 cm
- 8. The area of the base of a right circular cone is 154 cm 2 and its height 14 cm. The curved surface of the cone is?
Options- A. (154 x ?2 ) cm2
- B. 11 cm2
- C. (154 + ?7 ) cm2
- D. 5324 cm2 Discuss
Correct Answer: (154 x ?2 ) cm2
Explanation:
? 22/7 x r2 = 154
? r2 = 154 x (7/22) = 49
? r = 7 cm and h = 14
So, l = ?(7)2 + (14)2 = ?245 = 7?5 cm
? Area of curved surface = ?rl
= (22/7) x 7 x 7?5 cm2
= 154?5 cm2
- 9. Volume of a hemisphere is 19404 cubic cm. The total surface area is?
Options- A. 27772 sq. cm
- B. 4158 sq. cm
- C. 5544 sq. cm
- D. 1386 sq. cm Discuss
Correct Answer: 4158 sq. cm
Explanation:
(2/3) x (22/7) x r3 = 19404
? r3 = 19404 x (7/22) x (3/2) = 9261 = (21)3
? r = 21 cm
Total Surface area = 3?r2
= 3 x (22/7) x 21 x 21 cm2
= 4158 cm2
- 10. A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical balls, The diameter of two of these are 1.5 cm and 2 cm respectively. The diameter of the third ball is?
Options- A. 2.66 cm
- B. 2.25 cm
- C. 3 cm
- D. 3.5 cm Discuss
Correct Answer: 2.25 cm
Explanation:
? 4/3?r3 = 4/3? x [(3/2)3 - {(3/4)3 + 13 } ]
? r3 = 125/64 = (5/4)3
? r = 5/4
? Diameter = (5/4) x 2 cm = 2.5 cm.
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