Question

Related Rates Problem: The radius of a spherical watermelon is growing at a constant rate of 2 centimeters per week. The thickness of the rind is always one tenth of the radius. The volume of the rind is growing at the rate __?__ cubic centimeters per week at the end of the fifth week. Assume that the radius is initially zero.

Answer 1

im a bit rusty at this but ill try
vol of rind = (4/3) pi r^3 - (4/3) pi (0.9r)^4 = (4/3) pi 0.271 r^3
dv/dr = 4 pi 0.271 r^2
dr/dt = 2

dv/dt = dv/dr * dr/dt = 8 pi 0.271 r^2
at end of fifth week radius = 2*5 = 10

so rate of growth of vol of the rind = 8 pi 0.271 * 100 = 682 cu cms / week