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Question
A metallic hemisphere is melted and recast in the shape of a cone with the same base radius R as that of the hemisphere. If H is the height of the cone, then write the values of \[\frac{H}{R} .\]
Solution
Given,
Radius of the hemisphere = Radius of the cone.
Now,
Volume of the hemisphere `2/3 piR^3`
and
Volume of the cone `1/3 piR^2 H`
Volume of the hemisphere = volume of the cone
`2/3 piR^2 = 1/3 piR^2 H`
`2R = H` or `H/R = 2`
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