Discussion
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- Question
- 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
- Correct Answer
- 24300 m
ExplanationRadius 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 - 1. 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
- 2. 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
- 3. 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
- 4. 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
- 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
- 6. 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
- 7. 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
- 8. 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
- 9. If the height of a come is doubled, then its volume is increased by?
Options- A. 100%
- B. 200%
- C. 300%
- D. 400% Discuss
- 10. If the radius of a sphere is doubled, then its volume is increased by?
Options- A. 100 %
- B. 200 %
- C. 700 %
- D. 800 % Discuss
Volume and Surface Area problems
Search Results
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: 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
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: 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%
Correct Answer: 100%
Explanation:
Original volume = 1/3 ?r2h;
New volume = 1/3 ?r2(2h) = 2/3?r2h
Required increased % = [?r2h/3]/[?r2h/3] x 100%
= 100%
Correct Answer: 700 %
Explanation:
Original volume = 4/3?r3
New volume = 4/3 ? (2r)3 = 32/3 ?r3
Required increased % = [(28/3) ?r3] x [(3/4)?r3] x 100 % = 700 %
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