Volume and Surface Area problems
- 1. 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% Discuss
Correct Answer: 100/h%
Explanation:
Total 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 %
- 2. 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
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
- 3. 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
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 / ??
- 4. 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
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
- 5. 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
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
- 6. 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
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)
- 7. If each side of a cube is decreased by 19 %, then decrease in surface area of cube is?
Options- A. 40.4%
- B. 38.4%
- C. 35.6%
- D. 34.39% Discuss
Correct Answer: 34.39%
Explanation:
The net decrease in the surface area of the cube is given by
[x + y + xy/100] %
Here, x = y = 19%
= [-19 + (-19) + (-19) x (-19)/100] %
= [-38 + 361/100] %
= [-38 + 3.61] %= -34.39% (-ve sign implies for decrease)
- 8. If the height of the right circular cone is increased by 200% and the radius of the base is reduced by 50%. Then, the change in the volume of cone is?
Options- A. increase by 25%
- B. increase by 50%
- C. remains unchanged
- D. decreases by 25% Discuss
Correct Answer: decreases by 25%
Explanation:
From the formula the net change in volume is given as [x + y + z + (xy + yz + zx)/100 + xyz/(100)2 ] %
Here, x = 200, y = z = -50 (-ve sign for decrease)
= [ 200 + (-50) + (-50) + (200) x (-50) + (-50) x (-50) + (-50) x (200)/100 + (200) x (-50) x (-50)/(100)2 ] %
= 100 + (-10000 + 2500 - 10000)/100 + 500000/100 x 100 ] %
= [ 100 + (-17500)/100 + 50]%
= (150 - 175)% = -25% (-ve sign implies for a decrease )
So, the volume is decreased by 25%.
- 9. A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of water is raised by 6.75 cm. What is the radius of the ball?
Options- A. 6 cm
- B. 9 cm
- C. 8 cm
- D. None of these Discuss
Correct Answer: 9 cm
Explanation:
Volume of the spherical ball = Volume of the water displaced
? 4/3 ?r3 = ?(12)2 x 6.75
? r3 = 144 x 6.75 x 3/4 = 729
? r = 9 cm
- 10. A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm lowered into the water until it is completely immersed. The water level in the vessel will rise by?
Options- A. 4/9 cm
- B. 9/4 cm
- C. 2/3 cm
- D. 4/5 cm Discuss
Correct Answer: 9/4 cm
Explanation:
Volume of the sphere = Volume of the water displaced
Let the required height to which the water rises be h.
Then, ?r12h = 4/3 ?r23
? 16 h = 4/3 x 27 ? h = 36/16 = 9/4 cm
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