Question

If the volume and radius of the cone are $320\pi c{m}^3$ and $8cm$ respectively then find the total surface area of the cone.

Answer 1

volume = $320\pi$

$\Rightarrow \frac{1}{3}\pi r^{2}h=320\pi$

$\Rightarrow \frac{\pi }{3}(8{)}^{2}h=320\pi$

$\Rightarrow [h=15cm]$

$TSA=\pi r^2={\pi }^2+\pi rl$

$\Rightarrow TSA=\pi r(l=r)$

$\Rightarrow TSA=\pi \left(8\right)\left(\sqrt{r^2+h^2+8}\right)$

$\Rightarrow TSA=\pi \left(8\right)(\sqrt{8^2+{15}^2}+8)$

$\Rightarrow TSA=\pi \left(8\right)(17+8)$

$\Rightarrow [TSA=200\pi cm]$