Volume and Surface Area problems
- 1. If each edge of a cube is increased in increased by 50%, the percentage increase in surface area is?
Options- A. 50 %
- B. 75 %
- C. 100 %
- D. 125 % Discuss
Correct Answer: 125 %
Explanation:
Let original length of cube = L
Then, its surface area = 6L2
New edge = (150 x L)/10 = 3L/2
New surface area = 6 x (3L/2)2 = (6 x 9 x L2)/4 = (27/2) x L2
Increase in surface area = (27/2 - 6) x L2 = 15 x L2/2
? Increase percent = (15 x L2/2 ) / (6L2) x 100 % = 125 %
- 2. The difference in volumes of two cubes is 152 m 3 and the difference in their one face areas is 20 m 2. If the sum of their edge is 10 m, the product of their edge is?
Options- A. 21
- B. 24
- C. 36
- D. 48 Discuss
Correct Answer: 24
Explanation:
Let the edges of the two cubes be x and y metres
Then, x3 - y3 = 152
and x2 - y2 = 20
Also, x + y = 10
So, x - y = (x2 - y2) / (x + y) = 20/10 = 2
Now, (x3 - y3) / (x - y) = 152/2
? x2 + y2 + xy = 76
? (x + y)2 - xy = 76
? xy = (x + y)2 - 76 = (10)2 - 76 = 24
- 3. The sun of 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. 486 cm2 Discuss
Correct Answer: 236 cm2
Explanation:
? l + b + h = 19
and l2 + b2 + h2 = (5?5)2 = 125
? (l + b + h)2 = (19)2
? (l2 + b2+ h2) + 2(lb + bh + lh) = 361
? 2 (lb + bh + lh) = (361 - 125) = 236
? Surface area = 236 cm2
- 4. A tank 30 m long, 20 m wide and 12 m deep is dug in a field 500 m long and 30 m wide. By how much will the level of the field rise, if the Earth dug of the tank is evenly spread over the field?
Options- A. 0.33 m
- B. 0.5 m
- C. 0.25 m
- D. 0.4 m Discuss
Correct Answer: 0.5 m
Explanation:
Volume of the Earth taken out = 30 x 20 x 12
= 7200 m3
Area of the remaining portion (leaving the area of dug out portion) = 470 x 30 + 30 x 10
= 14100 + 300 = 14400 m3
Let h be height to which the field is raised by spreading the Earth dug out.
Then, 14400 x h = 7200
? h = 7200/14400 = 0.5 m
- 5. A right circular cone of height h is cut by a plane parallel to the base at a distance h/3 from the base, then the volumes of the resulting come and the frustum are in the ratio?
Options- A. 4/7
- B. 8/19
- C. 6/19
- D. 18/19 Discuss
Correct Answer: 8/19
Explanation:
The volume of the original cone is V = (?R2h)/3
The height and the radius of the smaller cone are 2h/3 and 2R/3, respectively
? 1/3? (2R/3)2 x 2h/3 = 8V/27
? Volume of the frustum = (V - 8V/27) = 19V/27
So, the required ratio is 8 : 19 .
- 6. 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
Correct Answer: 25%
Explanation:
If the radius remains unchanged
Then, x = y = 0 and z = 17.5 %
? Net increase in volume = 17.5%
- 7. 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
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
- 8. 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
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
- 9. 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
Correct Answer: 6
Explanation:
Let the side of cube be x .
Then, Volume of cube = Surface area of cube
? x3 = 6x2
? x = 6
- 10. 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
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
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