The volume of an expanding sphere is increasing at a rate of 12 𝑓𝑡3 𝑠 ⁄ .

Question

The volume of an expanding sphere is increasing at a rate of 12 ^𝑓𝑡3/s . When the volume of the sphere is

36𝜋 𝑓𝑡3 , how fast in ^𝑓𝑡2/s is the surface area increasing?

Hint: 𝑉 = 4/3 (𝜋𝑟 3) and 𝑆 = 4𝜋𝑟 2

Answer 1

Hi Hosea!

I've gone through the basic steps to get to the end answer (without explicitly telling you the answer). I'm happy to go much more in depth with related rates problems and the chain rule. Please contact me if you would like to talk more!