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

hey there!

if she's saving for six months, let's divide the total number we need for the trip by six, dividing it into the amount that needs to be saved for each month.

500 ÷ 6 =

she needs to save at least this amount each month, so we should use this symbol: ≥

let x be the amount she saves each month.

your final answer is x ≥

hope this !