Discussion
Home ‣ Aptitude ‣ Volume and Surface Area Comments
- Question
- 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
- Correct Answer
- 2h/3
ExplanationLet 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. - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. If the total surface area of a cube is 6 sq units, then what is the volume of the cube?
Options- A. 1 cu unit
- B. 2 cu units
- C. 4 cu units
- D. 6 cu units Discuss
- 8. If the volume of a cube is 729 cu cm, what is the length of its diagonal?
Options- A. 9?2 cm
- B. 9?3 cm
- C. 18 cm
- D. 18?3 Discuss
- 9. Find the surface area of a cuboid 10 m long, 5 m broad and 3 m high?
Options- A. 105 sq m
- B. 104 sq m
- C. 170 sq m
- D. 190 sq m Discuss
- 10. The surface area of a cube is 726 sq cm. Find the volume of the cube.?
Options- A. 1331 cm3
- B. 1232 cm3
- C. 1626 cm3
- D. 1836 cm3 Discuss
Volume and Surface Area problems
Search Results
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: 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: 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: (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
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: 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
Correct Answer: 1 cu unit
Explanation:
Total surface area of a cube = 6a2
? 6 = 6a2
? a2 = 1
? a = 1
Now, volume of the cube = a3 = 13 = 1 cu unit
Correct Answer: 9?3 cm
Explanation:
Volume of cube = (Side)3
? 729 = a3
? a = 9 cm
Diagonal of cube = side x ?3 = 9 x ?3
= 9?3 cm
Correct Answer: 190 sq m
Explanation:
Given that, l = 10 m , b = 5 m, h = 3 m
lb = 10 x 5 = 50, bh = 5 x 3 = 15,
lh = 10 x 3 = 30
? Surface area of a cuboid
= 2(lb + bh + lh)
= 2(50 + 15 + 30)
= 2 x 95 = 190 sq m
Correct Answer: 1331 cm3
Explanation:
According to the question,
6a2 = 726 [a = edge of the cube]
? a2 = 726/6 = 121
? a = ?121 = 11 cm
? Required volume = a3 = 113 = 1331 cm3
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