Instructions

Consider a solid torus. This is a donut$-$shaped object. Let the radius of the circle formed by going around the solid part of the donut be r$.$ Let the radius of the circle formed by going around the donut hole be R$.$ See the picture below.

When answering the questions below, make sure that you do what is expected. Write out your answers on paper neatly. Then, upload your work to Canvas through this assignment. You must only upload a single PDF file for me to look at$.$ To be clear, I will only offer bonus credit for this assignment if the instructions are followed exactly $($name on paper, neat work, numbered answers, submitted on time, one PDF file$).$

Questions

$(10$ points$)$ Setup the integral that expresses the volume of the torus as described above.

$(10$ points$)$ Calculate the volume, which results in a formula for the area of a solid torus regardless of radii values.