Question

Suppose R is the region bounded by y = x^2, x = 2, and y = 0. A solid is generated by revolving R about the x = 3. Find the volume of the solid.

Answer 1

What say you? How shall you proceed?

Answer 2

I'm struggling to apply the formula. I graphed it already, but I still don't know which method to use.

Answer 3

Take your pick. I like to do both, just for the practice.

Answer 4

If i use washer, my formula will be pi * the integral of outer radius squared - inner radius squared on the interval of 0 to 4, right? How do I determine R(y) and r(y)?

Answer 5

Outer: 3-x <== "x" is on the curve y = x^2
Inner: 3-2 = 1 <== This is constant. No need to use an integral. Geometry works.

Answer 6

does it look like \[\pi \int\limits_{0}^{4}[(3-\sqrt(y))^2 - 1^2 ]dy\]

Answer 7

That's it! Good work.