Solving an Application with a Cubic Function

Park rangers construct a mound of gravel in the shape of a cone with the height equal to twice the radius. The volume of the cone in terms of the radius is given by

$$V=\frac{2}{3}\pi r^3$$

Find the inverse of the function $V=\frac{2}{3}\pi r^3$ that determines the volume $V$ of a cone and is a function of the radius $r.$ Then use the inverse function to calculate the radius of such a mound of gravel measuring 100 cubic feet. Use $\pi =\mathrm{3.14.}$

OpenStax, Algebra and Trigonometry 2e · §5.7 Inverses and Radical Functions · Example 9