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 and volume of the frustum.
Solution:
Lateral surface area of frustum
$=\pi(\mathbf{r}+\mathbf{R}) \mathbf{l}$
$=\pi(5+8) \times 5$
$=204.28 \mathrm{~m}^{2}$
Height of cone
$h=\sqrt{5^{2}-(R-r)^{2}}$
$=\sqrt{5^{2}-(8-5)^{2}}$
$=\sqrt{13}$
Volume $=\frac{\pi \times \sqrt{13}}{3}\left(8^{2}+5^{2}+40\right)=540.56 \mathrm{~cm}^{3}$