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Question
The radii of two cones are in the ratio 2 : 1 and their volumes are equal. What is the ratio of their heights?
Solution
Let the radius of the first cone = 2x
And height of the first cone = h1
Then,
Volume of the first cone `=1/3 pir^2 h `
`=1/3 pi(2x) ^2 h_1 ` ............. (1)
The radius of the second cone = x
Height of the second cone = h2
Then,
Volume of the second cone `=1/3 pir^2 h `
`=1/3 pi(x) ^2 h_2 `
Since,
The volumes of the two cones are equal.
Or `h_1 :h_2 = 1 : 4`
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