Hello, User Name!

I'll number the formulas like this: .

Formula (1): .

. . is the area of the circle. . is the average of the two radii.

Therefore, (1) gives theareaof the "average circle".

. . I seriously doubt that this happens to be the volume of the doughnut.

Formula (3): .

. . is the volume of a sphere.

. . We have: .

This is the volume of a sphere of radius

. . plus the volume of a sphere of radius

. . divided by 4.

This is too large to be the volume of the doughnut.

Formula (4): .

We have: .

. . is the area of the outer circle.

. . is the area of the inner circle.

. . is the area of the "ring".

I don't think multiplying by will give us the volume of the dougnut.

Formula (5): .

We have: .

This the volume of a sphere of radius ... (quite large!)

. . multipled by

This is far too large to be the volume of the doughtnut.

By elimination, . .is the volume of the doughnut.