Discussion
Home ‣ Aptitude ‣ Volume and Surface Area Comments
- Question
- The Volume of a wall, 5 times as high as it is broad and 8 times as long as it is high, is 12.8 m 3. The breadth of the wall is?
Options- A. 30 cm
- B. 40 cm
- C. 22.5 cm
- D. 25 cm
- Correct Answer
- 40 cm
ExplanationLet breadth = L meters. Then, height = 5L meters and length = 40L meters
? L x 5L x 40L = 12.8
? L3 = 12.8/200 = 128/2000 = 64/1000
? L = 4/10
Thus, breadth = (4/10) m = (4 x 100)/10 cm = 40 cm - 1. The radius of a wire is decreased to one-third. If volume remains the same, length will increase?
Options- A. 1 time
- B. 2 times
- C. 6 times
- D. 9 times Discuss
- 2. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between the surface area of two solids is?
Options- A. 284 cm2
- B. 286 cm2
- C. 296 cm2
- D. 300 cm2 Discuss
- 3. Bricks are worth Rs. 750 per 1000 and their length, breadth and height 25 cm, 12.5 cm and 7.5 cm respectively. The cost of bricks required to build a wall 200 m long, 1.8 m high and 37.5 cm thick is?
Options- A. Rs. 42, 600
- B. Rs. 43, 200
- C. Rs. 40, 750
- D. Rs. 41, 860 Discuss
- 4. A river 2 m deep and 45 m wide is running at the rate of 3 km/hr. The amount of water that runs into the per minute is?
Options- A. 4500 m3
- B. 27000 m3
- C. 3000 m3
- D. 2100 m3 Discuss
- 5. The maximum length of a pencil that can be kept in a rectangular box of dimensions 8 cm x 6 cm x 2 cm is?
Options- A. 2 ?13 cm
- B. 2 ?14 cm
- C. 2 ?26 cm
- D. 10 ?2 cm Discuss
- 6. The volume of a sphere is 38808 cu. cm. The curved surface area of the sphere is?
Options- A. 5544 sq. cm
- B. 1386 sq. cm
- C. 8316 sq. cm
- D. 4158 sq. cm Discuss
- 7. A right cylindrical vessel is full with water. How many right cones having the same diameter and height as those of the right cylinder will be needed to store that water?
Options- A. 2
- B. 3
- C. 4
- D. 5 Discuss
- 8. A right cylinder and a right circular cone have the same radius and the same volume. The ratio of the height of the cylinder to that of the cone is?
Options- A. 3 : 5
- B. 2 : 5
- C. 3 : 1
- D. 1 : 3 Discuss
- 9. A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by?
Options- A. 4.5 cm
- B. 2.25 cm
- C. 4/9 cm
- D. 2/9 cm Discuss
- 10. The radius of a circular cylinder is the same as that of a sphere. Their volumes are equal. The height of the cylinder is?
Options- A. 4/3 times its radius
- B. 2/3 times its radius
- C. Equal to the radius
- D. Equals to its diameter Discuss
Volume and Surface Area problems
Search Results
Correct Answer: 9 times
Explanation:
Let original radius = r and original length = h
New radius = r/3
Let new length = H
Then, ? r2h = ? (r/3)2 x H = ? r2H/9
? H = 9h
Thus, the length becomes 9 times .
Correct Answer: 286 cm2
Explanation:
Volume of cube formed = 216 cm3
? Edge of the cube = (6 x 6 x 6)1/3 = 6 cm
Surface area of original metal sheet = 2(27 x 8 + 8 x 1 + 27 x 1) cm2 = 502 cm2
Surface area of the cube formed = [6 x (6)2] cm2 = 216 cm2
? Required difference in area of two solids = (502 - 216) cm2
= 286 cm2
Correct Answer: Rs. 43, 200
Explanation:
Number of bricks required = Volume of wall in cm3 / Volume of 1 brick
= (200 x 100 x 1.8 x 100 x 37.5)/(25 x 12.5 x 7.5)
= 57, 600
? Required cost = Rs. (750 x 57600)/1000
= Rs. 43, 200
Correct Answer: 4500 m3
Explanation:
Speed per min = (3 x 1000)/60 m = 50 m
Volume of water running per min. = (45 x 2 x 50) m2
= 4500 m3
Correct Answer: 2 ?26 cm
Explanation:
Length of pencil = ? [(8)2 + (6)2 + (2)2] cm
= ?104 cm
= 2?26
Correct Answer: 5544 sq. cm
Explanation:
? 4/3 x 22/7 x r3 = 38808
? r3 = (38808 x 7/22 x 3/4)
= (21)3
? r = 21 cm
So, curved surface area of sphere
= 4?r2
= (4 x 22/7 x 21x21) cm2
= 5544 cm2
Correct Answer: 3
Explanation:
Let N cones be needed
Then, 1/3 ?r2 h x N = ?r2h
? N = 3
Correct Answer: 1 : 3
Explanation:
Let the height of cylinder = h
and height cone = H
Then, ?r2 h = 1/3 ?r2 H
? h/H = 1/3 = 1 : 3
Correct Answer: 2.25 cm
Explanation:
? ? x (4)2 x h = 4/3 ? x (3)3
? h = 9/4 cm
= 2.25 cm
Correct Answer: 4/3 times its radius
Explanation:
? 4/3 ?r3 = ?r2 h
? h = 4/3 r
? Height = 4/3 times its radius.
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