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Solving an Application with a Cubic Function

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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= 2 3 π r 3 V = \frac{2}{3} \pi r^{3}

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

OpenStax Algebra and Trigonometry 2e, 5.7 Inverses and Radical Functions, exercise 23

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Adapted from College Algebra © 2021 Rice University. Licensed under CC BY 4.0. Sources: College Algebra 2e, Algebra and Trigonometry 2e, Precalculus 2e, College Algebra with Corequisite Support 2e. Imported at revision 4922e46.