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- Question
- If the volume of two right circular cones are in the ratio 1 : 3 and their diameters are in the ratio 3 : 5, then the ratio of their heights is?
Options- A. 25 : 27
- B. 1 : 5
- C. 3 : 5
- D. 5 : 27
- Correct Answer
- 25 : 27
ExplanationLet diameter, radius and height of first cone are d1, r1 and h1, respectively and that of second cone are d2, r2 and h2, respectively.
r1/r2 = d1/d2 = 3/5,
h1/h2 = ?
Given,
[(1/3)?r21h1] / [(1/3)?r22h2] = 1/3
? (3/5)2 x h1/h2 = 1/3
? h1/h2 = (1/3) x (25/9) = 25/27 - 1. If the height of the right circular cone is increased by 200% and the radius of the base is reduced by 50%, then the volume of the cone?
Options- A. increases by 25%
- B. increases by 50%
- C. remains unchanged
- D. decreases by 25% Discuss
- 2. The ratio of the radius and height of a cone is 5 : 12. Its volume is 314 2/ 7 cm 3. Its slant height is?
Options- A. 18 cm
- B. 13 cm
- C. 16 cm
- D. 15 cm Discuss
- 3. If the ratio of volumes of two cones is 2 : 3 and the ratio of the radii of their bases is 1 : 2, then the ration of their heights will be?
Options- A. 3 : 8
- B. 8 : 3
- C. 9 : 2
- D. 8 : 1 Discuss
- 4. The diameter of a right circular cone is 14 m, while its slant height is 9 m, Find the volume of the cone.?
Options- A. 49 ? ?32/3 m3
- B. 50 ? ?32/3 m3
- C. 3/49 ? ?32 m3
- D. ??32/9 m3 Discuss
- 5. The radius of the base of a right circular cone is doubled. To keep the volume fixed, the height of the come will be?
Options- A. half of the previous height
- B. one-third of the previous height
- C. one-fourth of the previous height
- D. 1/?2 times of the previous height Discuss
- 6. The diameters of two cones are equal. If their slant heights be in the ratio of 5 : 7, then find the ratio of their curved surface areas.?
Options- A. 25 : 7
- B. 25 : 49
- C. 5 : 49
- D. 5 : 7 Discuss
- 7. The radius of the base of a right circular cone is increased by 15% keeping the height fixed. The volume of the cone will be increased by.?
Options- A. 30%
- B. 31%
- C. 32.25%
- D. 34.75% Discuss
- 8. What is the diameter of the largest circle lying on the surface of a sphere of surface area 616 sq cm?
Options- A. 14 cm
- B. 10.5 cm
- C. 7 cm
- D. 3.5 cm Discuss
- 9. The diameter of the Moon is approximately one-fourth of the diameter of the Earth. What is the ratio (approximate) of their volumes?
Options- A. 4 : 16
- B. 1 : 64
- C. 1 : 4
- D. 1 : 128 Discuss
- 10. A sphere and a hemisphere have the same surface area. The ratio of their volumes is?
Options- A. ?3/4 : 1
- B. 3?3/4 : 1
- C. ?3/8 : 1
- D. 3?3/8 : 1 Discuss
Volume and Surface Area problems
Search Results
Correct Answer: decreases by 25%
Explanation:
Here, x = -50%, y = 200%
According to the formula Net effect
= [2x + y + x2 + 2xy/100 + x2y/1002] %
= [-100 + 200 + 2500 - 20000/100 + 500000/10000]%
= [100 - 175 + 50] % = -25%
Correct Answer: 13 cm
Explanation:
Let radius = 5k, height = 12k
According to the question
= 1/3 x 22/7 x (5k)2 x 12k = 2200/7
? k = 1
? r = 5, h = 12
? Slant height (l) = ?r2 + h2
= ?25 + 144
= ?169
=13 cm
Correct Answer: 8 : 3
Explanation:
[(1/3)?r12h1]/[(1/3)?r22h2] = 2/3
? (r1/r2)2 x (h1/h2) = 2/3
? (1/2)2 x (h1/h2) = 2/3 [ &bacaus; r1/r2 = 1/2]
? h1/h2 = 8/3
? h1 : h2 = 8 : 3
Correct Answer: 49 ? ?32/3 m3
Explanation:
Given, l = 9 m
and diameter = 14 m ? r = 14/2 = 7 m
Now, volume = (1/3)?r2h
= (1/3)? x 49 x ?l2 - r2
= (1/3)? x 49 x ?81 - 49
= (1/3) x 49? x ?32 = 49??32 /3 m3
Correct Answer: one-fourth of the previous height
Explanation:
In first situation.
Radius = r1, height = h1 and volume = v1
In second situation,
Radius =2r1, height = h2 and volume = v2
In the volume is fixed, then
v1 = v2
? (1/3)?r21h1 = (1/3)?(2r1)2h2
? h1 = 4h2
? h2 = h1/4
Therefore, height of the the cone will be one-fourth of the previous height.
Correct Answer: 5 : 7
Explanation:
Given, l1/l2 = 5/7
Now, curved surface area of the first cone = ? rl1
and curved surface area of second cone = ?rl2
? Ratio = ?rl1/?rl2 = l1/l2 = 5 : 7
Correct Answer: 32.25%
Explanation:
Let the fixed height of a right circular cone is h and initial radius is r
Then, initial volume of cone, V1 = (1/3)?r2h
After increasing 15% radius of a cone = (r + 3r/20) = 23r/20
New volume become, V2 = (1/3)?(23/20)2r2h
? Increasing percentage = [(V2 - V1) / V1] x 100
= {[(1/3)?r2h] / [(1/3)?r2h]} {(23/20)2 - 1} x 100
= (23/20 + 1)(23/20 - 1) x 100
= 43/20 x 3/20 x 100 = 32.25%
Correct Answer: 14 cm
Explanation:
Surface area of sphere = 6616 cm2
4?r2 = 6166
?r2 = (6166 x 7)/(4 x 22)
? r2 = 7 x 7
? r = 7 cm
? Diameter of largest circle lying on sphere = 2 x r = 2 x 7 = 14 cm
Correct Answer: 1 : 64
Explanation:
Given that, the diameter of moon is approximately one-fourth of the diameter of Earth.
Let radius on moon = r
Then, radius of Earth = 4r
? Volume of Moon/Volume of Earth
= [(4/3)?r3] / [(4/3)?(4r)3]
= [r3] / [64r3] = 1/64 = 1 : 64
Correct Answer: 3?3/8 : 1
Explanation:
According to the question,
Surface area of sphere = Surface area of hemisphere
4?r12 =3?r22
? r1/r2 = ?3/2
? Ratio in volume = [(4/3)?r13] / [(4/3)?r23]
= 3?3/8 : 1
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