Question

Curved surface area of a cone is $251.2c{m}^2$ and radius of its base is $8cm$. Find its slant height and perpendicular height. $(\pi =3.14)$

Answer 1

Let the perpendicular height and the slant height of the cone be $hcm$ and $Icm$ respectively
Radius of the base of cone $r=8cm$
Curved surface area of the cone $=251.2c{m}^2$
$\therefore \pi rl=251.2c{m}^2$
$\Rightarrow 3.14\times 8\times I=251.2$
$\Rightarrow l=\frac{251.2}{25.12}=10$
Now,
$r^2+h^2=I^2$
$\Rightarrow (8{)}^2+h^2=(10{)}^2$
$\Rightarrow 64+h^2=100$
$\Rightarrow h^2=100-64=36$
$\Rightarrow h=\sqrt{36}=6cm$
Thus, the slant height and perpendicular height of the cone is $10cm$ and $6cm$ respectively.