Discussion
Home ‣ Aptitude ‣ Volume and Surface Area Comments
- Question
- 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
- 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 - 1. 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
- 2. 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
- 3. 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
- 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
- 5. 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
- 6. 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
- 7. 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
- 8. The cost of painting the four walls of a room is Rs. 350. The cost of painting a room three times in length, breadth and height respectively will be?
Options- A. Rs. 1050
- B. Rs. 1400
- C. Rs. 3150
- D. Rs. 4200 Discuss
- 9. A solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is h. If the total volume of the cone, then the height of the cylinder is?
Options- A. 2h
- B. 4h
- C. 2h/3
- D. 3h/2 ?r2 x 5 Discuss
- 10. The diagonal of a cube is 2? 3 cm. Find the surface area of the cube.
Options- A. 15 sq cm
- B. 18 sq cm
- C. 25 sq cm
- D. 24 sq cm Discuss
Volume and Surface Area problems
Search Results
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
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
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: 18 cm
Explanation:
? 1/3 ? x (2)2 x h = ? x (2)2 x 6
? h = 18 cm
Correct Answer: 15 cm
Explanation:
? (1/3)?r2 x h = ?r2 x 5
? h = 15 cm
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
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.
Correct Answer: Rs. 3150
Explanation:
Area of 4 walls of the room = [2 (l + b ) x h ]m2
Area of 4 walls of new room = [2 (3l + 3b) x 3h]m2
= 9 x [2(l + b) x h ]m2
? Cost of painting the 4 walls of the new room = Rs. (9 x 350)
= Rs. 3150
Correct Answer: 2h/3
Explanation:
Let the height of the cylinder be H and its radius = r
Then, (?r2 H) + (1/3) x (?r2h) = 3 x (1/3)?r2h
? ?r2H = (2/3)?r2h
? H = 2h/3.
Correct Answer: 24 sq cm
Explanation:
Given, diagonal = 2?3
? a?3 = 2?3 [a = edge of the cube]
? a = 2
? Required surface area = 6a2
= 6 x 22 = 24 sq cm
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