Question

The slant height of a right circular cone is $10\text{cm}$ and its height is $8\text{cm}$, then the area of its curved surface is:

• A. $80\pi {\text{cm}}^2$
• B. $60\pi {\text{cm}}^2$
• C. $65\pi {\text{cm}}^2$
• D. $70\pi {\text{cm}}^2$

Answer 1

The correct option is B $60\pi {\text{cm}}^2$

Given, slant height of a right circular cone, $l=10\text{cm}$

and its height, $h=8\text{cm}$.

Then the radius of the cone will be,

$\begin{array}{cc}{r}^2& =l^2-h^2\\ & =(10{)}^2-(8{)}^2\\ & =100-64\\ & =36\\ r& =6\text{cm}\end{array}$

Therefore, the curved surface area of right circular cone,

$\begin{array}{cc}\text{C.S.A of a cone}& =\pi rl\\ & =\pi \times 6\times 10\\ & =60\pi {\text{cm}}^2\end{array}$

Hence, option $B$ is correct.