# Math Help - Hot-Air Balloon Surface Area

1. ## Hot-Air Balloon Surface Area

The surface area S (in square meters) of a hot air balloon is given by:

S(r) = 4(pi)(r^2), where r is the radius of the balloon (in meters).

If the radius r is increasing with time t (in seconds) according to the formula
r(t) = (2/3)(t^3), where t is > or = to 0, find the surface area S of the balloon as a function of the time t.

2. Originally Posted by symmetry
The surface area S (in square meters) of a hot air balloon is given by:

S(r) = 4(pi)(r^2), where r is the radius of the balloon (in meters).

If the radius r is increasing with time t (in seconds) according to the formula
r(t) = (2/3)(t^3), where t is > or = to 0, find the surface area S of the balloon as a function of the time t.
Hello,

r is a function of t, S is a function of r. Compose both function so that S is a function of t:

$S(r(t))=4 \cdot \pi \cdot \left(\frac{2}{3} \cdot t^3 \right)^2$. Expand the bracket:

$S(t)=\frac{16}{9} \cdot \pi \cdot t^6$

EB

3. ## ok

This is exactly what I wanted you to do with the other two questions.

Thanks!