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____$m$.

• 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

Given that,
$\pi \times {50}^2=\pi \times r_1\times l$

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

$\Rightarrow l=100m$

Slant height is given by

$l^2=h^2+r_1^2$

$h^2=l^2-r_1^2$

$puttingl=100$,

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

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