Question

A drinking glass is in the shape of a frustum of a cone of height $14\mathrm{cm}$. The diameters of its two circular ends are $4\mathrm{cm}$ and $2\mathrm{cm}$. Find the capacity of the glass.

Answer 1

Given : Height of frustum$\left(\mathrm{h}\right)=14\mathrm{cm}$

Radius of larger circle $\left(\mathrm{R}\right)=\frac{4}{2}=2\mathrm{cm}$

Radius of smaller circle $\left(\mathrm{r}\right)=\frac{2}{2}=1\mathrm{cm}$

Therefore,

$\begin{array}{rcl}\mathrm{Capacity}\mathrm{of}\mathrm{glass}& =& \mathrm{Volume}\mathrm{of}\mathrm{Frustum}\\ & =& \frac{1}{3}\mathrm{\pi h}({\mathrm{r}}^2+{\mathrm{R}}^2+\mathrm{rR})\\ & =& \frac{1}{3}\times \mathrm{\pi }\times 14\left(\right(1\times 1)+(2\times 2)+(2\times 1\left)\right)\\ & =& \frac{1}{3}\times \frac{22}{7}\times 14\times 7\\ & =& 102.67{\mathrm{cm}}^3\end{array}$

Hence, capacity of glass is $102.67{\mathrm{cm}}^3$