Question

What is the total surface area of a cone, if its radius $=5cm$ and height = $\sqrt{2}cm$?

• A. $159.983{mm}^2$
• B. $159.983{cm}^2$
• C. $159.983cm$
• D. $159.983m^2$

Answer 1

The correct option is B $159.983{cm}^2$

We know, slant height is:

$s^2=h^2+r^2$, where $h=$ height of cone and $r=$ radius of the base of the cone.

Given, $h=\sqrt{2}cm$ and $r=5cm$.

$\therefore s^2={\sqrt{2}}^2+5^2=2+25=27$

$\Rightarrow s^2=27$

$\Rightarrow s=\sqrt{2}7$

$\Rightarrow s=5.19cm$.

Then, total Surface area of cone$=\pi rs+\pi r^2$

Here, $\pi =3.14$, $r=5cm$ and $s=5.19cm$.

$\therefore$ Total surface area $=\pi rs+\pi r^2$

$=3.14\times 5\times 5.19+3.14\times 5\times 5$

$=81.483+78.5$

$=159.983c{m}^2$.

Hence, option $B$ is correct.