Question

The radii of the ends of a frustum of a right circular cone are $5$ metres and $8$ metres and its lateral height is $5$ metres. Find the lateral surface area and volume of the frustum.

Answer 1

Given, radii of the ends of a frustum are $r=5m$ and $R=8m$

Lateral height $l=5m$

LSA of frusturn$=\pi (R+r)l$

$=\frac{22}{7}(8+5)\times 5m^2$

$=204.29m^2$

Height $h=\sqrt{l^2-{(R-r)}^2}$

$=\sqrt{5^2-{(8-5)}^2}m$

$=\sqrt{16}m$

$=4m$

Volume of the frustum $=\frac{1}{3}\pi h(R^2+r^2+Rr)$

$=\frac{1}{3}\times \frac{22}{7}\times 4(8^2+5^2+8\times 5)$

$=\frac{1}{3}\times \frac{22}{7}\times 4\times 129$

$=540.57m^2$

Hence, the lateral surface area is $204.29m^2$ and volume is $540.57m^2$.