Question

Suppose a < b and (x - b)^2 + y^2 <(or equal to) a^2 is the disk of radius a centered at (b; 0).
Revolving this disk around the y-axis gives a doughnut shape object called a torus.
Find the volume of this torus in terms of a and b.

Answer 1

I honestly dont know where to start. Never really seen on like this

Answer 2

there are several ways ( at least two i can think of) to solve this.
I will give you the intuitive one with explanations.

so basically they took a cylinder with radius "a" of some length "L" and bent it into a ring/doughnut/torus in such a way that the symmetry line of the cylinder makes a perfect circle of radius "b" around the y-axis on the xz plane.
The volume of a cylinder is an easy one : Volume=length*area = \[L*\pi*a^2\]
What we will have to find out is : what is L?
L is actually the circumference of that circle that the center line of the bent-cylinder makes.
the radius of which is given - "b". Thus:
\[L=2\pi*b\]
which means :
\[Volume=2\pi*b*\pi*a^2=2\pi^2*b*a^2\]

more info and graphics are here:
http://en.wikipedia.org/wiki/Torus

Answer 3

So will i even have a number answer? Or just that? Sorry never seen a problem like this so having problem with the concept.

Answer 4

Easy: look at the question. They ask you to produce the answer "in terms of a and b". which in math language means "use the parameters we told you to use and any known math constants
"

Answer 5

if you tell me what makes this question hard i can explain.

Answer 6

I appreicate the help, I think with your equation I understand it well. Thanks!