Question

The area of the base of a cone is $616$ sq.cm. Its height is $48cm$. What is its total surface area ?

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

Answer 1

Answer: (A)

$2816{cm}^2$

We know, the base of a cone is circular.

Then, Area of a circle $=\pi r^2=616$.
$\Rightarrow r^2=\frac{616\times 7}{22}=196$
$=>r=14cm$.
Also, total surface area of a cone $=\pi r(r+l)$
where, $r$ is the radius of the cone and $l$ is the slant height.

For a cone, slant height $l=\sqrt{r^2+h^2}$

where, $h$ is the perpendicular height.

Hence, $l=\sqrt{{48}^2+{14}^2}=\sqrt{2500}$

$⟹$ $l=50cm$.
Hence, Total surface area of this cone, $=\frac{22}{7}\times 14\times (14+50)=2816{cm}^2$.

Therefore, option $A$ is correct.