Question

Given a cone with a volume of 288 in and height 7 in find the base radius of the cone

Answer 1

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ ------\\ h=7\\ V=288 \end{cases}\implies 288=\cfrac{\pi \cdot r^2\cdot 7}{3} \\\\\\ \cfrac{288\cdot 3}{7\pi }=r^2\implies \sqrt{\cfrac{288\cdot 3}{7\pi }}=r$