Let V be the volume of the region bounded between two expanding concentric spheres. at time t = 0 the spheres have radii of 6 cm and 40 cm. The radius of the smaller sphere is increasing at a rate of 8 cm/sec, while the radius of the larger sphere is increasing at a rate of 2 cm/sec. At what value of t (t>0) will the volume V be a maximum?
I had no idea to set this problem up because I don't know how to install the variable "t". The book set up the equation as v = (4/3)pi(40+2t)^3 - (4/3)pi(6+8t)^3.
I'm just hoping that someone can make sense out of the equation, how the radii were replaced by expressions with "t".