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 16 cm and 12 cm. Find the capacity of the glass.

Answer 1

We have,

The height of the frustum, h = 14 cm,

Base radii, $R=\frac{16}{2}=8$ cm and $r=\frac{12}{2}=6$ cm

The capacity of the glass = Volume of the frustum

$=\frac{1}{3}\pi h(R^2+r^2+rR)=\frac{1}{3}\times \frac{22}{7}\times 14\times (8^2+6^2+8\times 6)=\frac{1}{3}\times 22\times 2\times (64+36+48)=\frac{44}{3}\times 148=\frac{6512}{3}c{m}^3\approx 2170.67c{m}^3$

So, the capacity of the glass is $2170.67c{m}^3$