Calculus: Assuming that a soap bubble retains its spherical

[Kristi02]

Hello everyone,
I am new to the site and could really use some help. I am having trouble figuring out how to go about some word problems. Please help.

Assuming that a soap bubble retains its spherical shape as it expands, how fast is its radius increasing when its radius is 2 inches, if air is blown into it at the rate of 4 cubic inches per second?
I think that I need to use the area of a circle, but other than that, I am at a loss. I have a final this Wednesday and would appreciate any help I can get to learn how to do these type of problems.
Thanks,
Kristi

 

[galactus]

Not a circle, a sphere.

The volume of a sphere is given by \(\displaystyle V=\frac{4}{3}{\pi}r^{3}\)

You want \(\displaystyle \frac{dr}{dt}\) given \(\displaystyle \frac{dV}{dt}=4 \;\ and \;\ r=2\)

Differentiate the volume formula with respect to time, sub in your given values and solve for \(\displaystyle \frac{dr}{dt}\)

 

[Kristi02]

Thanks so much for your help. I will try this and see if I can figure it out.