Question

A circular ground of radius 50 m has to be covered with a waterproof sheet. The same amount of waterproof sheet is also used for making a conical tent. If the base area of the tent is 625 $\pi m^2$, then the height of the tent is____$cm$.

• A. 90.42
• B. 96.8
• C. 100.6
• D. 88.5

Answer 1

The correct option is B

96.8

Let $r_1$ be the radius of the tent

$\Rightarrow$ $\pi {r_1}^2=625\pi$

$\Rightarrow {r_1}^2=625$

$\Rightarrow r_1=25$ m

We know that
$\pi {50}^2=\pi rl$

${50}^2=25\times l$
$\Rightarrow l=100$ m

We know that, slant height $=\sqrt[2]{2\left(h^2\right)+\left({r1}^2\right)}=\sqrt[2]{2\left(h^2\right)+\left({25}^2\right)}=100$

$h^2=\sqrt{{100}^2-{25}^2}$

$h=\sqrt[2]{29375}=96.82$ cm