A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are $3.5\ cm$ and $7\ cm$ respectively. Find the height to which the water will rise in the cylinder.

 Given:

A vessel in the form of a hemispherical bowl is full of water. Its contents are emptied in a right circular cylinder. The internal radii of the bowl and the cylinder are $3.5\ cm$ and $7\ cm$ respectively.

To do:

We have to find the height to which the water will rise in the cylinder.

Solution:

Radius of the hemispherical bowl $(r) = 3.5\ cm$

This implies,

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

$=\frac{2}{3} \pi \times(3.5)^{3}$

$=\frac{2}{3} \pi(3.5)(3.5)(3.5)$

$=\frac{85.75}{3} \pi \mathrm{cm}^{3}$

Volume of water in the cylindrical vessel $=\frac{85.75}{3} \pi$

Radius of the vessel $(\mathrm{R})=7 \mathrm{~cm}$

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

$=\frac{85.75 \pi}{3 \times \pi \times 7 \times 7}$

$=\frac{1.75}{3}$

$=\frac{7}{4 \times 3}$

$=\frac{7}{12} \mathrm{~cm}$

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Updated on: 10-Oct-2022

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