Question

If the lateral surface area of a frustum of a right circular cone is $560\pi c{m}^2$ and radii of its ends are 8 cm and 20 cm, then its height is

• A. 12 cm
• B. 16 cm
• C. 18 cm
• D. 14 cm

Answer 1

The correct option is B 16 cm

Let $r_{1}and{r}_2$ be the radii of ends of the frustum and $h$ be the height.

$\therefore r_1=20cm,r_2=8cm,LSA=560\pi c{m}^2.$

$\therefore \text{LSA of frustum}=\pi (r_1+r_2)\times \sqrt{(r_1-r_2{)}^2+h^2}$

$\Rightarrow 560\pi =\pi \times (20+8)\times \sqrt{(20-8{)}^2+h^2}$

$\Rightarrow 20=\sqrt{{12}^2+h^2}$

$\Rightarrow h^2={20}^2-{12}^2=400-144=256$

$\Rightarrow h=\sqrt{256}=16cm$

Hence, the correct answer is option (b).