(a) Set up an integral for the volume a solid torus (the donut-shaped solid shown in the figure) with radii br and aR. (Let a = 8 and b = 8.)
(b) By interpreting the integral as an area, find the volume V of the torus.

Question

(a) Set up an integral for the volume a solid torus (the donut-shaped solid shown in the figure) with radii br and aR. (Let a = 8 and b = 8.)
(b) By interpreting the integral as an area, find the volume V of the torus.

ihannah_banana7 · Answer

attachment

zepdrix · Answer

Ooo the donut! This is a fun one.

zepdrix · Answer

|dw:1475273591417:dw|

ihannah_banana7 · Answer

aR-br?

loser66 · Answer

*

ihannah_banana7 · Answer

Can we go through the process of solving it?

ihannah_banana7 · Answer

Would you change the $$1- (\sin \theta)^2$$ to $$(\cos \theta)^2$$

ihannah_banana7 · Answer

Yeah not very fun.

ihannah_banana7 · Answer

Would it have been possible to do Integration by Parts before putting x in terms of theta?

ihannah_banana7 · Answer

On my online assignment they had us make the limits from 0 to 8r. So maybe that would help?

zepdrix · Answer

I have a feeling I made a mistake somewhere in here.
It shouldn't take this long to get through :[

Sec imma look up solution for torus,
see if I made a boo boo.

ihannah_banana7 · Answer

Okay. Yeah this just seems so complicated for one problem.

zepdrix · Answer

Ok from what I'm reading, washer method is supposedly easier for this problem. So lemme wiz through that a sec and see what it looks like :d

zepdrix · Answer

|dw:1475276579705:dw|We want to split the circle into left and right sides, so we solve for x this time.$$\large\rm x=aR\pm\sqrt{(br)^2-y^2}$$