Question

The curved surface area of the frustum of a cone is 180 sq. cm and the circumference of its circular bases are 18 cm and 6 cm respectively. Find the slant height of the frustum of a cone.

Answer 1

Let the radii of the circular ends be r₁ cm and r₂ cm.
Given:
Curved surface area of the frustum of the cone = 180 cm²
Also,
Circumference of the small end (C₁) = 6 cm
$\Rightarrow$2$\mathrm{\pi }$ r₁ = 6
$\Rightarrow$r₁= $\frac{3}{\mathrm{\pi }}$
And,
Circumference of the large end (C₂) = 18 cm
$\Rightarrow$2$\mathrm{\pi }$ r₂ = 18
$\Rightarrow$r₂= $\frac{9}{\mathrm{\pi }}$
Now,
Curved surface area of the frustum of the cone = $\mathrm{\pi }$(r₁ + r₂)l
$\Rightarrow$180 = $\mathrm{\pi }\left(\frac{3}{\mathrm{\pi }}+\frac{9}{\mathrm{\pi }}\right)l$
$\Rightarrow$180 = 12l
$\Rightarrow$l = 15 cm

Thus, the slant height of the frustum of the cone is 15 cm.