Question

The area of the base of a cone is $616c{m}^2$ and its height is $48cm$. The total surface area of cone is:

• A. $2816c{m}^2$
• B. $2861c{m}^2$
• C. $2618c{m}^2$
• D. $2681c{m}^2$

Answer 1

The correct option is A $2816c{m}^2$

Given, the area of the base of a cone is $616c{m}^2$.

If $r$ be the radius of the base of the cone,

then $\pi r^2=616$.

$⟹$ $\frac{22}{7}\times r^2=616$

$⟹$ $r=14$.

Also, given height $\left(h\right)=48cm$.

Then slant height $\left(l\right)=\sqrt{{48}^2+{14}^2}=2\sqrt{625}=50cm$.

$\therefore$ Total surface area of the cone $=\pi r(r+l)=\frac{22}{7}\times 7(14+50)=\frac{22}{7}\times 14\times 64=2816c{m}^2$.

Hence, option $A$ is correct.