Question

Total surface area of a cone is $616sq.cm$ If the slant height of the cone three times the radius of its base, find its slant height.

Answer 1

Let the radius of base and slant height of the cone $r$ cm and $l$ cm, respectively.
Slant height of the cone $=3\times$Radius of the cone (given)
$\therefore l=3r$
Total surface area of the cone $=616c{m}^2$
$\therefore \pi r(r+l)=616c{m}^2$
$\Rightarrow \frac{22}{7}\times r\times (r+3r)=616$
$\Rightarrow \frac{22}{7}\times r\times 4r=616$
$\Rightarrow \frac{88}{7}{r}^2=616$
$\Rightarrow r^2=\frac{616\times 7}{88}=49$
$\Rightarrow r=\sqrt{49}=7cm$
$\therefore$ Slant height of the cone, $l=3r=3\times 7=21cm$
Thus, the slant height of the cone is $21cm$.