A torus is formed by rotating a circle of radius r about a line in the plane of the circle that is a distance R (> r) from the center of the circle. Find the volume of the torus.

Consider a circle with radius centered at some point on the -axis. This circle has equation

Revolve the region bounded by this circle across the -axis to get a torus. Using the shell method, the volume of the resulting torus is

where .

So the volume is

Substitute

and the integral becomes

Notice that is an odd function, so the integral over is 0. This leaves us with

Write

so the volume is

points are handed out whenever you post answers.

brainliest answers are handed out by the person asking the question, so whether your answer is picked depends entirely on whether the asker bothers to pick

if you're asking about your rank, it depends on having a certain number of points and a certain number of brainliest answers. for example, at the time of this writing, i have 44338 points out of 15000 needed for the next (nearly triple the requirement! ) but i only have 24 out of 50 required brainliest answers. this number decays, meaning after a certain amount of time (i think about a month), the total number of brainliest answers you've earned doesn't count toward this total. (i've been stuck at the same rank for a long

the lesson to learn here is that you shouldn't worry about points or rank. chances are, no matter how good an answer you may provide, your efforts will go mostly unnoticed unless you focus on the newest/most active questions that get posted.

i think that you should ask google for the answer to that problem because if we don't know it google does