Question

The ratio of slant height and the radius of a cone is $7:4$. If its lateral surface area is $792{cm}^2$, then find its radius.

Answer 1

Given, slant height (I) : radius ( $r$ ) $=7:4$
$\Rightarrow \frac{l}{r}=\frac{7}{4}$
$\Rightarrow l=\frac{7}{4}r\dots$(i)
And its lateral surface area $=792{cm}^2$
$\Rightarrow \pi rl=792$
$\Rightarrow \frac{22}{7}\times r\times \frac{7}{4}r=792$
$\Rightarrow \frac{22\times 7}{4\times 7}{r}^2=792$
$\Rightarrow r^2=\frac{792\times 4}{22}$
$=\frac{3168}{22}=144$
$\Rightarrow r=\sqrt{144}=12cm$
Hence, radius of the cone $=12cm$