# The slant height of the frustum of a cone is 4 cm

Question:

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

Solution:

The slant height of the frustum of the cone is = 4 cm. The perimeters of the circular ends are 18 cm and 6 cm. Let the radii of the bottom and top circles are r1 cm and r2 cm respectively. Then, we have

$2 \pi r_{1}=18$

$\Rightarrow \pi r_{1}=9$

$2 \pi r_{2}=6$

$\Rightarrow \pi r_{2}=3$

The curved surface area of the frustum cone is

$=\pi\left(r_{1}+r_{2}\right) \times l$

$=\left(\pi r_{1}+\pi r_{2}\right) \times l$

$=(9+3) \times 4$

= 48 Square cm