Posted by **Erica** on Tuesday, October 3, 2006 at 12:18pm.

The surface ares S (in square meters) of a hot air ballon is given by s(r)=4 pi r^2 where r is radius of balloon (in meters). If the radius r is increasing with time (in seconds) according to the formula r(t) = 2/3t^3, t is greater than or equal to 0, find the surface area S of the balloon as a function of the time t.

Ok, your first function give S(r) or surface area as a function of the radius. You second function r(t)=(2/3)t^3 gives the radius as a function of time. If you compose the function to get

S(r(t)) = 4*pi*((2/3)t^3)^2

you have the surface area as a function of time alone. You can write it as

S(t) = something you can simplify.

## Answer This Question

## Related Questions

- Calculus - t: 0 2 5 7 11 12 r'(t): 5.7 4.0 2.0 1.2 0.6 0.5 The volume of a ...
- Math - A spherical balloon expands uniformly as it is inflated. The radius of ...
- Physics - A hot air balloon of radius 12 meters has been heated so that the air ...
- calculus - You are letting the air out of a hot air balloon at a steady rate. ...
- calculus - a splenical ballon is being inflated @ 10 cubic inches per secound. ...
- Word Problem - The surface area of a balloon is given by S(r) = 4(pie)r^2, where...
- math - If the radius of a circular wave is increasing at 2 meters/sec, how fast ...
- physics - A ball is released from a hot air balloon moving downward with a ...
- physics - A ball is released from a hot air balloon moving downward with a ...
- physics - A ball is released from a hot air balloon moving downward with a ...

More Related Questions