Question

A dish in the shape of a frustum of a cone has a height of $6$cm. Its top and its bottom have radii of $24$cm and $16$cm respectively. Find its curved surface area. ( in $c{m}^2$)

• A. $200\pi$
• B. $300\pi$
• C. $400\pi$
• D. $500\pi$

Answer 1

The correct option is C $400\pi$

Curved surface area of a frustum of a cone $=\pi l(r_1+r_2)$

where $l$ is the slant height of the cone $=\sqrt{h^2+{(r_1-r_2)}^2}$
$h$ is the height
$r_1$ and $r_2$ are the radii of the lower and upper ends of a frustum of a cone.
So, $l=\sqrt{6^2+{(24-16)}^2}$
$l=10cm$
Hence, Curved Surface area of this frustum of a cone $=\pi \times 10\times (24+16)=400\pi {cm}^2$