Question

what is the exact circumference of the base of a cone that has a volume of 1014 pi in^3 and a height of 18 in.

Answer 1

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ -----\\ V=1014\pi \\ h=18 \end{cases}\implies 1041\pi =\cfrac{\pi \cdot r^2\cdot 18}{3} \\\\\\ 1041\pi =6\pi r^2\implies \cfrac{1041\pi }{6\pi }=r^2\implies \cfrac{347}{2}=r^2\implies \boxed{\sqrt{\cfrac{347}{2}}=r}\\\\ -------------------------------\\\\ \textit{circumference of a }\stackrel{cone's}{circle}\\\\ C=2\pi r\qquad \qquad C=2\pi \left( \boxed{\sqrt{\cfrac{347}{2}}} \right)$