Question

A vessel is in the form of a hemispherical bowl mounted by a hollow cylinder. The diameter of the sphere is $14cm$ and the total height of the vessel is $13cm$. Find its capacity. (Take $\pi =22/7$)

Answer 1

Let $r$ be the radius of the hemispherical bowl and $h$ be the height of the cylinder.

Then, $r=7cm$ and $h=6cm$

Total capacity of the bowl

$=$ volume of the cylinder + volume of the hemisphere
$=(\pi r^{2}h+\frac{2}{3}\pi r^3){cm}^3$

$=\pi r^2(h+\frac{2}{3}r){cm}^3$

$=\frac{22}{7}\times 7^2\times (6+\frac{2}{3}\times 7){cm}^3$

$=1642.66{cm}^3$