I need help understanding the process to combine terms to result in a specific function. I have a cylinder with the volume and surface area defined below:
The book is asking: Assume that the volume of the cylinder is 1000 cm^3. Express the surface area as a function of the radius. After combining terms in your answer, show that the resulting function can be written:
S(r) = (2(Pi)(r^2) + 2000)/r where (r>0)
I understand that the problem is looking for S(r), where 2(Pi)(r^2)+2(Pi)rh is the formula for the surface area, but I don't understand how the book ends up with the resulting function.