The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm,

Solution:

Greater radius = R = 33 cm
Smaller radius = r = 27 cm
Slant height = l = 10 cm

Using the formula for height of a frustum:

Height =  h =

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

$=\sqrt{10^{2}-(33-27)^{2}}$

$=\sqrt{100-(6)^{2}}$

$=\sqrt{100-36}$

$=\sqrt{64}=8 \mathrm{~cm}$

Capacity of the frustum

$=\frac{1}{3} \pi h\left(R^{2}+r^{2}+R r\right)$

$=\frac{1}{3} \times \frac{22}{7} \times 8\left(33^{2}+27^{2}+33 \times 27\right)$

$=\frac{22 \times 8}{3 \times 7} \times 2709=22704 \mathrm{~cm}^{3}$

Surface area of the frustum

$=\pi R^{2}+\pi r^{2}+\pi l(R+r)$

$=\pi\left[R^{2}+r^{2}+l(R+r)\right]$

$=\frac{22}{7}\left[33^{2}+27^{2}+10(33+27)\right]$

$=\frac{22}{7}[1089+729+10(60)]$

$=\frac{22 \times 2418}{7}=7599.43 \mathrm{~cm}^{2}$