Question

A frustum of a right circular cone is of height $16$ cm with radii of its ends as $8$ cm and $20$ cm has lateral surface area equal to

• A. $540\pi c{m}^2$
• B. $580\pi c{m}^2$
• C. $560\pi c{m}^2$
• D. $680\pi c{m}^2$

Answer 1

The correct option is C $560\pi c{m}^2$

Curved Surface area of a frustum of a cone $=\pi l(r_1+r_2)$ where $l$ is the slant height $=\sqrt{h^2+{(r_1-r_2)}^2}$ $h$ is the height.
$r_1$ and $r_2$ are the radii of the lower and upper ends of a frustum of a cone.

So, $l=\sqrt{{16}^2+{(20-8)}^2}$

$\therefore l=20cm$
Hence, Curved surface area of this frustum of a cone $=\pi \times 20\times (20+8)=560\pi {cm}^2$