Question

The radius and slant height of a cone are in the ratio of 4 : 7. If its curved surface area is 792 $c{m}^2$ then its radius is (Use $\pi =22/7$)

• A. 8 cm
• B. 10 cm
• C. 12 cm
• D. 6 cm

Answer 1

Answer: (C)

12 cm

Let r cm be the radius and l cm be the slant height of the cone Then.
r:l=4:7$\Rightarrow$r=4xcm l=7xcm
Now curved surface area =792$c{m}^2$
$\Rightarrow \pi rl=792\Rightarrow \frac{22}{7}\times 4x\times 7x=792$
$x^2=\frac{792}{88}=9\Rightarrow x=3$
$\therefore r=4xcm=12cm$
Hence the radius of the base of the cone is 12 cm