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If the radius of the cone is doubled, keeping the height constant, what is the ratio of the volume of the smaller cone to larger cone?
- a)2:9
- b)5:7
- c)1:4
- d)1:7
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the radius of the cone is doubled, keeping the height constant, wha...
v1/v2 = (r1²) * h1 / (r2²) * h2 (h1=h2)
(r)²/(2r)²
v1/v2 = 1:4
(r)²/(2r)²
v1/v2 = 1:4
Most Upvoted Answer
If the radius of the cone is doubled, keeping the height constant, wha...
Solution:
Let the radius of the smaller cone be 'r' and its height be 'h'. Then, its volume will be given by V1 = (1/3)πr²h.
When the radius is doubled, the new radius will be '2r' and the height will remain the same as 'h'. The volume of the larger cone will be V2 = (1/3)π(2r)²h = (4/3)πr²h.
The ratio of the volumes of the smaller cone to the larger cone will be V1/V2 = [(1/3)πr²h]/[(4/3)πr²h] = 1/4.
Therefore, the ratio of the volume of the smaller cone to the larger cone is 1:4, which is option C.
Note: It is important to understand the formula for the volume of a cone and how it changes with a change in radius or height. In this question, we only changed the radius and kept the height constant, but in other questions, we may need to change both variables, so it is important to understand the impact of these changes on the volume.
Let the radius of the smaller cone be 'r' and its height be 'h'. Then, its volume will be given by V1 = (1/3)πr²h.
When the radius is doubled, the new radius will be '2r' and the height will remain the same as 'h'. The volume of the larger cone will be V2 = (1/3)π(2r)²h = (4/3)πr²h.
The ratio of the volumes of the smaller cone to the larger cone will be V1/V2 = [(1/3)πr²h]/[(4/3)πr²h] = 1/4.
Therefore, the ratio of the volume of the smaller cone to the larger cone is 1:4, which is option C.
Note: It is important to understand the formula for the volume of a cone and how it changes with a change in radius or height. In this question, we only changed the radius and kept the height constant, but in other questions, we may need to change both variables, so it is important to understand the impact of these changes on the volume.
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