Question

The volume of a right circular cone is $320\pi c{m}^3$ and the radius of its base is $8cm$. Find its slant height, curved surface area, and total surface area. Give your answers in terms of $\pi$.

Answer 1

Volume of the cone $=\frac{1}{3}\pi r^{2}h=320\pi$ {Given}

$=\frac{1}{3}\pi \times 8^2\times h=320\pi$

It gives: $h=15cm$

We know that slant height follows this relation: $l^2=r^2+h^2$

$=8^2+{15}^2=289$

It gives: $l=17cm$

Now, $CSA=\pi \times r\times l$

$=\pi \times 8\times 17=136\pi c{m}^2$

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

$=\pi \times 8\times (8+17)$ $=200\Pi c{m}^2$