College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 2 - Section 2.5 - Variation - 2.5 Assess Your Understanding: 17

Answer

$\color{blue}{V=\dfrac{4\pi}{3}r^3}$

Work Step by Step

RECALL: (1) If $y$ varies directly as $x$, then $y=kx$ where $k$ is the constant of proportionality. (2) If $y$ varies inversely as $x$, then $y=\dfrac{k}{x}$ where $k$ is the constant of proportionality. Notice that when the variation is direct, the variable is on the numerator while if the variation is inverse, the variable is in the denominator. The volume $V$ varies directly with the cube of the radius $r$ with a constant of proportionality $k$ of $\frac{4\pi}{3}$. Thus, the equation of the variation is: $\color{blue}{V=\dfrac{4\pi}{3}r^3}$
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