Question

Write a formula for the surface area (in square meters) of the balloon after seconds.

Answer 1

The formula for the surface area N(t) can be found by using r = P(t) in the expression for S(t):

$\begin{gathered} N(t)=S(P(t))=4\pi\lbrack P(t)\rbrack^2=4\pi(\frac{7}{3}t)^2=\frac{4\pi49}{9}t^2=\frac{196\pi}{9}t^2 \\ \\ N(t)=\frac{196\pi}{9}t^2 \end{gathered}$