Question

A cone with a height of 4 in, and a diameter of 6 in. Find the surface area and Volume​

Answer 1

if its diameter is 6, then its radius is half that or 3.

$\textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h }{3}~~ \begin{cases} r=radius\\ h=height\\[-0.5em] \hrulefill\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi (3)^2(4)}{3}\implies V=12\pi \\\\[-0.35em] ~\dotfill\\\\ \textit{surface area of a cone}\\\\ SA=\pi r\sqrt{r^2+h^2}+\pi r^2\qquad \implies \qquad SA=\pi (3)\sqrt{3^2+4^2}+\pi (3)^2 \\\\\\ 3\pi \sqrt{25}+9\pi \implies 3\pi (5)+9\pi \implies 15\pi +9\pi \implies 24\pi$