Question:
The radii of the circular ends of a frustum are 6 cm and 14 cm. If its slant height is 10 cm, then its vertical height is
(a) 6 cm
(b) 8 cm
(c) 4 cm
(d) 7 cm
Solution:
Radii of circular ends of frustum
$r_{1}=14 \mathrm{~cm}, r_{2}=6 \mathrm{~cm}$
Slant height
$I=10 \mathrm{~cm}, h=?$
$l=\sqrt{h^{2}+\left(r_{1}-r_{2}\right)^{2}}$
$l^{2}=h^{2}+\left(r_{1}-r_{2}\right)^{2}$
{squaring on both sides}
$h^{2}=l^{2}-\left(r_{1}-r_{2}\right)^{2}$
$h^{2}=(10)^{2}-(14-6)^{2}$
$h^{2}=100-64$
$h^{2}=36$
$h=6 \mathrm{~cm}$
Hence, the correct answer is choice (a).