Question

What is the total surface area of a right circular cone of height $14cm$ and base radius $7cm$?

• A. $344.35c{m}^2$
• B. $462c{m}^2$
• C. $498.35c{m}^2$
• D. None of these

Answer 1

Answer: (C)

We know, the total surface area of a right circular cone $=\pi r(r+l)$.

Given, base radius $r=7cm$.

Also, height $h=14cm$.

Then, slant height $l=\sqrt{h^2+r^2}$

$\Rightarrow l=(\sqrt{{14}^2+7^2}$

$\Rightarrow l=\sqrt{245}cm=7\sqrt{5}$ cm.

Now substitute the value in above equation, we have,

the total surface area $=\pi \times 7(7+7\sqrt{5})$

$=\frac{22}{7}\times 7\times 7(1+\sqrt{5})$

$=154(1+\sqrt{5})=498.35c{m}^2$.

Therefore, option $C$ is the correct.