Question

a torus (donut) having inner radius $2$ and outer radius $4$ sits on a flat table. what is the radius of the largest spherical ball that can be placed on top of the center torus so that the ball still touches the horizontal plane? (if the $xy$-plane is the table, the torus is formed by revolving the circle in the $xz$-plane centered at $(3,0,1)$ with radius $1$ about the $z$-axis. the spherical ball has its center on the $z$-axis and rests on either the table or the donut.)

Answer 1

The radius of the largest spherical ball that can be placed on top of the center torus is 2 units.

Step-by-step explanation:

To find the radius of the largest spherical ball that can be placed on top of the center torus, we need to consider the dimensions of both the torus and the ball. The torus has an inner radius of 2 and an outer radius of 4. The ball's radius should be equal to the difference between the outer radius of the torus and the radius of the torus itself. Therefore, the radius of the largest spherical ball that can be placed on top of the center torus is 2 units.