Say true or false.
A cone, a hemisphere and a cylinder stand on equal bases and have the same height. The ratio of their volumes is $1 : 2 : 3$ .

True

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False

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Solution

The correct option is A True
Volume of the cone $= \frac{1}{3} π r^{2} h$
Volume of the hemisphere $= \frac{2}{3} π r^{3}$
Volume of the cylinder $= π r^{2} h$
height s of all are same.
Height of hemisphere is $r$ , so is of cone and cylinder.
Therefore, $V_{1} = \frac{1}{3} π r^{2} r$
$V_{2} = \frac{2}{3} π r^{3}$
and $V_{3} = π r^{2} r$
So, it is true.

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