the radius of a large balloon is increasing at a rate of 2 inches per second. how fast, in cubic inches per second is the volume increasing when the radius is 10.

Answer 1

Here we have another optimization problem. Remember the key is to come up with the formula for what we are optimizing and take the derivative.

We assume the balloon is spherical which gives us V = 4/3πr³

Now we take the derivative (using the chain rule):

dV/dt = dV/dr * dr/dt = 4πr² * dr/dt

Now we just plug in numbers!

dV/dt = 4π(10)² * 2 = 800π in³/sec