Question

The slant height of a frustum of a cone is $4cm$ and the perimeters (circumference) of its circular ends are $18cm$ and $6cm$. Find the curved surface area of the frustum.

Answer 1

Given:

$l=4$ cm

Circumference of a circular end =$18$ cm

$\Rightarrow 2\pi r_1=18$

$\Rightarrow \pi \times r_1=\frac{18}{2}=9$ ...............................(1)

Circumference of other circular end $=6$ cm

$\Rightarrow 2\pi r_2=6$

$\Rightarrow \pi r_2=\frac{6}{2}=3$..........................................(2)

Adding (1) and (2)

Curved surface area

$=\pi (r_1+r_2)l$

$=(9+3)\times 4$

$=48$ cm${}^2$