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Question

Two right circular cones X and Y are made X having 3 times the radius of Y and Y having half the volume of X. Calculate the ratio between the heights of X and Y.

Solution
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Let radius of cone Y = r
Therefore, radius of cone X = 3r
Let volume of cone Y = V
Therefore, volume of cone X = 2V
Let h1 be the height of X and h2 be the height of Y.
Therefore,
Volume of cone X = 13π(3r2)h1 = 3πr2h1
Volume of cone Y = 13πr2h2
Therefore,
2VV=9h1h2
h1h2=29
h1:h2=2:9

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