- #1

togame

- 18

- 0

## Homework Statement

Find the volume of the torus formed when the circle of radius 2 centered at (3,0) is revolved about the y-axis. Use geometry to evaluate the integral.

## Homework Equations

Formula for the semi-circle: [itex]y=\sqrt{4-x^2}[/itex]

Solving for x give [itex]x=\pm\sqrt{4-y^2}[/itex]

## The Attempt at a Solution

I was thinking of solving the integral from -2 to 2 using both the positive and negative sides, then evaluate the integral and then multiply by 2, but I'm not so sure about my equation.

[tex]2\int_{-2}^2\pi\big( (3-\sqrt{4-y^2})^2 - (3+\sqrt{4-y^2})^2 \big) \mathrm d y[/tex]

I just seem lost on this one :(