Question

The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its capacity and total surface area. $[Use\pi =\mathrm{3.14.}]$

Answer 1

Greater radius = R = 33 cm

Smaller radius = r = 27 cm

Slant height = l = 10 cm

Using the formula for the height of a frustum:

Height $=h=\sqrt{l^2-(R-r{)}^2}=\sqrt{{10}^2-(33-27{)}^2}=\sqrt{{10}^2-(6{)}^2}=\sqrt{100-36}=\sqrt{64}=8$cm

The capacity of the frustum

$=\frac{1}{3}\pi h(R^2+r^2+Rr)=\frac{1}{3}\times \frac{22}{7}\times 8({33}^2+{27}^2+33\times 27)=\frac{(22\times 8)}{(3\times 7)}\times 2709=22704c{m}^3$

The surface area of the frustum

$=\pi R^2+\pi r^2+\pi l(R+r)=\pi [R^2+r^2+l(R+r\left)\right]=\frac{22}{7}[{33}^2+{27}^2+10(33+27\left)\right]=\frac{22}{7}[1089+729+10(60\left)\right]=\frac{22\times 2418}{7}=7599.43c{m}^2$