A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively $6\ cm$ and $4\ cm$. Find the height of water in the cylinder.

 Given:

A cylinder whose height is two-thirds of its diameter has the same volume as a sphere of radius $4\ cm$.

To do:

We have to find the height of water in the cylinder.

Solution:

Radius of the hemispherical bowl $(r) = 6\ cm$

Therefore,

Volume of water in the bowl $=\frac{2}{3} \pi r^{3}$

$=\frac{2}{3} \pi(6)^{3}$

$=\frac{2}{3} \times 216 \pi$

$=144 \pi \mathrm{cm}^{3}$

Volume of water in the cylinder $=144 \pi \mathrm{cm}^{3}$

Radius of the cylinder $(R)=4 \mathrm{~cm}$

Therefore,

Height of the cylinder $=\frac{\text { Volume }}{\pi r^{2}}$

$=\frac{144 \pi}{\pi \times 4 \times 4}$

$=9 \mathrm{~cm}$

Hence, the height of water in the cylinder is $9 \mathrm{~cm}$.

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Updated on: 10-Oct-2022

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