Question
A cone and a sphere have equal radii and equal volumes . Find the ratio of the diameter of the sphere to the height of the cone .
Answer: Option A
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Let radius of each be R and height of the cone be H.
Then , ` 4/3 pi R^3 = 1/3 pi R^2 H`
or` R/H = 1/4 or (2R)/(H) = 2/4 = 1/2`
`:.` Required ratio = 1 : 2 .
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