# Find the volume of the solid

1. May 27, 2010

### regnar

Find the volume of the solid obtained by rotating the region bounded by the given curves about the line y=1.

y = $$\sqrt[4]{x}$$ , y = x

I couldn't figure out if a should subtract one from x or from y = $$\sqrt[4]{x}$$. I don't know if I'm doing this right I tried subtracting it from x and got a negative area.

I also used this formula:
$$\pi$$$$\int$$r^2 h

2. May 27, 2010

### Staff: Mentor

Re: Volume

This formula is to be used when your typical volume element is a circular disk of radius r and thickness h. It is not at all applicable in this problem. Have you drawn a sketch of the region bounded by the two curves? Have you drawn a sketch of the solid generated when the region is rotated around the line y = 1? These sketches are necessary in helping you understand how to set up your integral. In this problem there are two approaches: cylindrical shells or circular washers.