# first ever post:

• Nov 7th 2012, 09:04 AM
KiloTango327
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.
• Nov 7th 2012, 06:06 PM
Soroban
Re: first ever post:
Hello, KiloTango327!

Quote:

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

From what I can tell, it is an optimization problem looking to minimize volume: .$\displaystyle V \:=\: \pi\int^b_a \big[f(x)-c\big]^2\,dx$

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