Answer
$\pi\frac{16}{9}t^6.$
Work Step by Step
$S(r)=4\pi r^2$ and $r(t)=\frac{2}{3}t^3$.
Therefore $S(r(t))=4\pi \left(\frac{2}{3}t^3\right)^2=\pi\frac{16}{9}t^6.$
Precalculus (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0-32197-907-9
ISBN 13:
978-0-32197-907-0
Chapter 5 - Exponential and Logarithmic Functions - 5.1 Composite Functions - 5.1 Assess Your Understanding - Page 255: 59
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