I'm struggling with a word problem

Question

The surface area S (in square meters) of a hot air balloon is given by S(r) = 4πr2 where r is the radius of the balloon (in meters). If the radius r is increased with time t (in seconds) according to the formula r (t) = 2/3 t3, t>0, find the surface area S of the balloon as a function of the time t.

Answer 1

You are given:

 

S=4πr²

 

r=(2/3)t³

 

Substitute the second equation in the first.

 

S=4π[(2/3)t³]²

 

S=4π(4/9)t⁶