Question

The curved surface area of of a right cone is $286m^2$ and its slant height is $13m$, then area of the base is:

• A. $308m^2$
• B. $286m^2$
• C. $154m^2$
• D. $187m^2$

Answer 1

Answer: (C)

We know, the curved surface area of a cone $=\pi rl$, where $r$ is the radius of the cone and $l$ is the slant height.

Given, the curved surface area of the cone $=286m^2$.

Hence, the curved surface area of this cone:

$\Rightarrow$ $\frac{22}{7}\times r\times 13=286[\because \pi =\frac{22}{7}]$
$\Rightarrow r=7m$.

We know, base of a cone is circular.

$\therefore$ Area of the base $=\pi r^2$

$=\frac{22}{7}\times 7\times 7$

$=154m^2$.

Hence, option C is correct.