Answer
See below.
Work Step by Step
By the text of the exercise $S(r)=S(r(t))=S(t)=4\pi r^2=4\pi r^2(t)=4\pi (\frac{2}{3}t^3)^2=4\pi \frac{4}{9}t^6=\frac{16\pi}{9}t^6$
College Algebra (10th Edition)
by Sullivan, Michael
Published by
Pearson
ISBN 10:
0321979478
ISBN 13:
978-0-32197-947-6
Chapter 6 - Section 6.1 - Composite Functions - 6.1 Assess Your Understanding - Page 409: 59
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