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(in $c{m}^3$).

• A. $\frac{308}{3}$
• B. $\frac{316}{3}$
• C. $\frac{301}{3}$
• D. $\frac{320}{3}$

Answer 1

The correct option is A

$\frac{308}{3}$

Height of frustum of cone = h = 14 cm

Radius of one end = r1 = 1 cm

Radius of the other end = r2 = 2 cm
Volume of the frustum
$=\frac{1}{3}\pi .h\left(\right(r1{)}^2+(r2{)}^2+(r1).(r2\left)\right)$
$=\frac{1}{3}\times \frac{22}{7}\times 14(1^2+2^2+(1\left)\right(2\left)\right)$
$=\frac{1}{3}\times \frac{22}{7}\times 14\times 7=\frac{308}{3}=102\frac{2}{3}c{m}^3$