Discussion
Home ‣ Aptitude ‣ Volume and Surface Area Comments
- Question
- The length, breadth and height of a room are l, b and h, respectively. The perimeter of the ceiling expressed as a percentage of the total area of the four walls, is?
Options- A. 100h%
- B. 100/h%
- C. h%
- D. h/100%
- Correct Answer
- 100/h%
ExplanationTotal area of four walls = 2h(l + b)
Perimeter of the celling = 2l + 2b = 2(l + b)
Perimeter of the ceiling in percentage = 2(l +b ) x 100/2h(l + b) %
= 100/h % - 1. A rectangular tank has 2.6 cu m of water. If the area of the base of the tank is 6500 sq cm, then the depth of water (in m) is?
Options- A. 3.5
- B. 4
- C. 5
- D. 8 Discuss
- 2. If the number representing volume and surface area of a cube are equal, then the length of edge of a cube in terms of the unit of measurement will be?
Options- A. 3
- B. 4
- C. 5
- D. 6 Discuss
- 3. The sum of length, breadth and depth of a cuboid is 19 cm and its diagonal is 5? 5 cm. Its surface area would be?
Options- A. 361 m2
- B. 125 m2
- C. 246 m2
- D. 486 m2 Discuss
- 4. The sum of the length, breadth and depth of a cuboid is 19 cm and its diagonal is 5? 5 cm, its surface area is?
Options- A. 361 cm2
- B. 125 cm2
- C. 236 cm2
- D. None of these Discuss
- 5. If height of a cylinder is increased by 17.5 % while its radius remains unchanged, by what percent does its volume increase?
Options- A. 17.5%
- B. 18%
- C. 19.8%
- D. 25% Discuss
- 6. A rectangular sump of dimension 6 m x 5 m x 4 m is to be built by using bricks to make the outer dimension 6.2 m x 5.2 m x 4.2 m. Approximately how many bricks of size 20 cm x 10 cm x 5 cm are required to build of size 20 cm x 10 cm 5 cm are required to build the sump for storing water?
Options- A. 15408
- B. 15409
- C. 16408
- D. 15448 Discuss
- 7. A sphere and a cube have the same surface area. The ratio of the volume of the sphere to that of the cube is?
Options- A. 1 : 2
- B. ?6 : ??
- C. 6 : ?
- D. 3 : 1 Discuss
- 8. A rectangular tank measuring 5 m x 4.5 m x 2.1 m is dug in the centre of the field measuring 13.5 m x 2.5 m . The Earth dug out is spread evenly over the remaining portion of the field. How much is the level of the field raised?
Options- A. 4.02 m
- B. 4.10 m
- C. 4.20 m
- D. 4.30 m Discuss
- 9. The base radius and height of a cone are doubled. The ratio of the new volume to original volume is?
Options- A. 8 : 7
- B. 8 : 3
- C. 8 : 1
- D. 8 : 5 Discuss
- 10. If radius of sphere is decreased by 24%. By what per cent does the surface area decrease?
Options- A. 44%
- B. 49%
- C. 42.24%
- D. 46.2% Discuss
Volume and Surface Area problems
Search Results
Correct Answer: 4
Explanation:
Volume of the tank = 2.6 cu m
Base area of the tank = 6500 cm = 0.65 sq m
? Depth of the tank = 26/0.65 = 4m
Correct Answer: 6
Explanation:
Let the side of cube be x .
Then, Volume of cube = Surface area of cube
? x3 = 6x2
? x = 6
Correct Answer: 246 m2
Explanation:
L + B + H = 19 cm, where L is the length, B is the breadth and
H is the height of the cuboid.
? (?L2 + B2 + H2
= (5?5)
On squaring both sides, we get
L2 + B2 + H2 + = 125
(L + B + H)2 = L2 + B2 + H2 + 2LB + 2LH + 2BH
? (19)2 = 125 + 2(LB + LH + BH)
? Surface area = 2(LB + LH + BH)
= 192 = 125 + 2(LB + LH + BH)
= 192 - 125 = 361 - 125 = 192 - 125
= 361 - 125 = 236 cm2
Correct Answer: 236 cm2
Explanation:
Let x, y and z be the length breadth and deapth of a cuboid.
? x + y + z = 19
x2 + y2 + z2 = (5?5)2 = 125
Surface area of the cuboid = 2(xy + yz + zx)
= (x + y + z)2) - (x2 + y2 + z2)
= 361 - 125 = 236 cm3
Correct Answer: 25%
Explanation:
If the radius remains unchanged
Then, x = y = 0 and z = 17.5 %
? Net increase in volume = 17.5%
Correct Answer: 15408
Explanation:
The volume that is needed to built by the bricks
= Volume of outer dimensions of sump - Volume of sump
= 6.2 x 5.2 x 4.2 - 6 x 5 x 4
= 135.408 - 120 = 15.405 m3
Volume of one brick = 20/100 x 10/100 x 5/100 = 0.01 m3
? Total number of bricks required to build the sump
= 15.408 / 0.001 = 15408
Correct Answer: ?6 : ??
Explanation:
Let r be the radius of the sphere and a be the side of the cube
? 4? r2 = 6a2
r = ?6 a / 2??
? r3 = 6?6a3 / 8???
? Ratio of volume = (4/3 ?r3)/a3
? Required ratio = ?6 / ??
Correct Answer: 4.02 m
Explanation:
Volume of Earth dug out = 5 x 4.5 x 2.1 = 47.25 m2
Area over which Each is spread = 13.5 x 25 - 5 x 4.5
= 33.75 - 220 = 11.75 m
Rise in level = 47.25/11.75 = 4.02 m
Correct Answer: 8 : 1
Explanation:
Let original radius = r and height = h
Original volume = (1/3)?r2h
New radius = 2r and new height = 2h
? New volume = 1/3 x ?(2r)2 x 2h = 8/3?r2h
Required ratio = 8/3?r2h : 1/3?r2h = 8 : 1
Correct Answer: 42.24%
Explanation:
The decrease in volume is given [ x + y + xy/100 ] %
Here , x = y = -24
= [(-24) + (-24) + (-24) x (-24)/100] %
= [-48 + 576/100] % = -48 + 5.76 = - 42.24 %
(-ve sign denotes decrease in volume)
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