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Question
A solid consists of a circular cylinder with an exact fitting right circular cone placed at the top. The height of the cone is h. If the total volume of the solid is 3 times the volume of the cone, then the height of the circular is
Options
2h
\[\frac{2h}{3}\]
\[\frac{3h}{2}\]
4h
Solution
Let r be the radius of the base of solid.
Clearly,
The volume of solid = 3 × volume of cone
Vol. of cone + Vol. of cylinder = 3 Volume of cone
Vol. of cylinder = 2 Vol. of cone
`pir^2 x = 2 xx 1/3 pi r^2 h`
`x = 2/3 h`
Thus,
The height of cylinder `= (2h)/3`
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