Volume and Surface Area problems
- 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
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 .
- 2. 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 Discuss
Correct Answer: 40 cm
Explanation:
Let 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
- 3. 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
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
- 4. 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
Correct Answer: 3
Explanation:
Let N cones be needed
Then, 1/3 ?r2 h x N = ?r2h
? N = 3
- 5. 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
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
- 6. 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
Correct Answer: 2.25 cm
Explanation:
? ? x (4)2 x h = 4/3 ? x (3)3
? h = 9/4 cm
= 2.25 cm
- 7. 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
Correct Answer: 4/3 times its radius
Explanation:
? 4/3 ?r3 = ?r2 h
? h = 4/3 r
? Height = 4/3 times its radius.
- 8. A hollow garden roller 63 cm wide with a girth of 440 cm is made of iron 4 cm thick. The volume of iron used is?
Options- A. 56372 cubic m
- B. 107712 cubic cm
- C. 54982 cubic cm
- D. 57636 cubic cm Discuss
Correct Answer: 107712 cubic cm
Explanation:
? Circumference of the girth = 440 cm
? 2?r = 440
? r = 440 / (2 x 7/22) = 70 cm
Thus, Outer radius = 70 cm
Inner radius = (70 - 4) cm = 66 cm
Volume of iron = ?[(70)2 - (66)2] x 63 cm3
= (22/7) x 136 x 4 x 63 cm3
= 107712 cm 3
- 9. The number of solid spheres each of diameter 6 cm that could be moulded to form a solid metal cylinder 4 cm, is?
Options- A. 3
- B. 4
- C. 5
- D. 6 Discuss
Correct Answer: 5
Explanation:
Let the number of spheres be N
Then, N x 4/3 ? x (3)3 = ? x (2)2 x 45
? 36N = 180
? N = 180/36 = 5
- 10. The length of the wire of 0.2 mm radius that can be drawn after melting a solid copper sphere of diameter 18 cm, is?
Options- A. 24.3 m
- B. 243 m
- C. 2430 m
- D. 24300 m Discuss
Correct Answer: 24300 m
Explanation:
Radius of sphere = 9 cm
Volume of sphere = [ 4/3 x ? x (9)3] cm3 = 972? cm3
Radius of wire = 0.2 mm = 2/(10 x 10) cm = 1/50 cm
Let the length of wire be = L cm
Then, 972? = ? x (1/50)2 x L
? L = (972 x 50 x 50 ) cm
?972? = ? x (1/50)2 x L
? L = (972 x 50 x 50) cm
? Length of wire = (972 x 50 x 50)/100 m = 24, 300 m
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