Thread: first ever post:

Hi. My name is Kelsey. I am a student at RIT currently taking project base calc 2. I am currently tasked with a rather challenging problem:


Suppose R is the region bounded by the curves y = f(x) and y = c, on the interval from a to b. Find the value of c that minimizes the volume of the solid that is generated by revolving R about the line y = c.


From what I can tell, it is an optimization problem looking to minimize volume: V = the integral from a to b of pi times (f(x)=c)²

All Im looking for is a nudge in the right direction as to how I would solve this problem.

Hello, KiloTango327!

Suppose is the region bounded by the curves and , on the interval
Find the value of that minimizes the volume of the solid that is generated by revolving about the line

From what I can tell, it is an optimization problem looking to minimize volume: .

I'd say you understand the problem . . . and your game plan is correct.