Discussion
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- Question
- 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
- 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 - 1. 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
- 2. 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
- 3. 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
- 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
- 5. 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
- 6. 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
- 7. 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
- 8. The height of cylinder is 14 cm and its curved surface area is 264 sq. cm. The volume of the cylinder is?
Options- A. 308 cm3
- B. 396 cm3
- C. 1448 cm3
- D. 1232 cm3 Discuss
- 9. The percentage increased in the surface area of a cube when each side is doubled, is?
Options- A. 25%
- B. 50%
- C. 150%
- D. 300% Discuss
- 10. If the radius of a sphere is doubled, then its surface area is increased by?
Options- A. 100%
- B. 200%
- C. 300%
- D. 50% Discuss
Volume and Surface Area problems
Search Results
Correct Answer: 4/3 times its radius
Explanation:
? 4/3 ?r3 = ?r2 h
? h = 4/3 r
? Height = 4/3 times its radius.
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: 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: 3
Explanation:
Let N cones be needed
Then, 1/3 ?r2 h x N = ?r2h
? N = 3
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: 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
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
Correct Answer: 396 cm3
Explanation:
? 2?rh = 264
? 2 x (22/7) x r x 14 = 264
? r = 3
So, Volume = ?r2h
= (22/7) x 3 x 3 x 14 cm3
= 396 cm3
Correct Answer: 300%
Explanation:
Original area = 6a2
New area = 6(2a)2 = 24a2
Required increased % = (18a2/6a2) x 100%
= 300%
Correct Answer: 300%
Explanation:
Original area = 4? r2,
New area = 4?(2r)2 = 16 ? r2
Required increased % = [12?r2]/[4? r2] x 100 %= 300%
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