Question:
The slant height of the frustum of a cone is 5 cm. If the difference between the radii of its two circular ends is 4 cm, write the height of the frustum.
Solution:
Slant height of the Frustum = 5 cm
i.e. $l=5 \mathrm{~cm}$.
$r_{1}-r_{2}=4 \mathrm{~cm}$
$l=\sqrt{h^{2}+\left(r_{1}-r_{2}\right)^{2}}$
$5=\sqrt{h^{2}+(4)^{2}}$
Squaring both sides we get
$25=h^{2}+4^{2}$
$25=h^{2}+16$
$25-16=4^{2}$'
or $h^{2}=9 \mathrm{~cm}$
$4=3 \mathrm{~cm}$
Height of the Frustum = 3 cm
$r_{1}-r_{2}=4 \mathrm{~cm}$