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((7)/(3)t)^2=(4\pi49)/(9)t^2=(196\pi)/(9)t^2 \\ \\ N(t)=(196\pi)/(9)t^2 \end{gathered}`