Question

Find the total surface area of a cone, whose $d=14\text{cm}$, $h=24\text{cm}$.

• A. $504{\text{cm}}^2$
• B. $3696{\text{cm}}^2$
• C. $704{\text{cm}}^2$
• D. $528{\text{cm}}^2$

Answer 1

Answer: (C)

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

Given, diameter of the cone $=14\text{cm}$.

Then, radius $r=\frac{d}{2}=\frac{14}{2}=7\text{cm}$.

Also, height $h=24\text{cm}$.

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

$\Rightarrow l=\sqrt{{24}^2+7^2}$

$\Rightarrow l=25\text{cm}$.

Now substitute the value in above equation, we have,

the total surface area $=\pi \times 7(7+25)$

$=\frac{22}{7}\times 7\left(32\right)$

$=704{\text{cm}}^2$.

Therefore, option $C$ is correct.