Question

Gas is escaping from a spherical balloon at a rate of 10ft^3/hour. At what rate is the radius changing when the volume is 400 ft^3?

Ok so dv/dt= 10ft^3/hr, V=400, and the equation for Volume of a sphere is V=(4/3)pi(r^3).

So do i rewrite the equation? in a way such as r=cubed root(v/((4/3)pi)? or do i differentiate it as is? I tried differentiating it as is, and got dv/dt=4pi(r^2)dr/dt, then solved for dr/dt. The only problem was i don't know what to do with the r value.

Any push in the correct direction would be appreciated.

Answer 1

well without calculus you can find the radius of a sphere given the volume, right?

Answer 2

ohh so just find the radius in the original equation with the given volume? Then plug it in after differentiating the original equation?

Answer 3

yup :)

Answer 4

Well thank you very much!

Answer 5

no problem!