Question:
The radii of the circular ends of a frustum of height 6 cm are 14 cm and 6 cm, respectively. Find the slant height of the frustum.
Solution:
We have,
Height of the frustum, $h=6 \mathrm{~cm}$,
Radii of the circular ends, $R=14 \mathrm{~cm}$ and $r=6 \mathrm{~cm}$
Let the slant height of the frustum be $l$.
Now,
$l=\sqrt{(R-r)^{2}+h^{2}}$
$=\sqrt{(14-6)^{2}+6^{2}}$
$=\sqrt{8^{2}+6^{2}}$
$=\sqrt{64+36}$
$=\sqrt{100}$
$=10 \mathrm{~cm}$
So, the slant height of the frustum is 10 cm.