Question

The volume of a cylinder is 4πx3 cubic units and its height is x units. Which expression represents the radius of the cylinder, in units?

Answer 1

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h\qquad \begin{cases} r=radius\\ h=height\\ -----\\ V=4\pi x^3\\ h=x \end{cases}\implies 4\pi x^3=\pi \cdot r^2\cdot x \\\\\\ \cfrac{4\pi x^3}{\pi x}=r^2\implies \implies 2^2x^2=r^2\implies \sqrt{2^2x^2}=r\implies 2x=r$