Question

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

Answer 1

Given:
Upper base diameter, D $=4$ cm
Lower base diameter, d $=2$cm
Height, h $=14$ cm
So, R (upper base) $=2$ cm,

r(lower $=1$cm

Capacity of glass = Volume of frustum of cone

$=\frac{\pi h}{3}[R^2+Rr+r^2]$

$=\frac{\pi \times 14}{3}[2^2+2\times 1+1^2]$

$=\frac{22\times 14[4+1+2]}{3\times 7}$

$=\frac{308}{3}=102\frac{2}{3}$cm ${}^3$

So, the capacity of the glass is $102\frac{2}{3}$ cm${}^3$