the ratio of the volume of a torus to its surface area is 3:2, find the radius of its cross-section

Question

Topic ,(solids of revolution and composite solids)

Answer 1

The volume of a torus with cross-sectional radius r and radius of torus is R (average of internal and external radii) is (pi)r^2*2(pi)R (think of torus as a cylinder bent into a circle with ends joined); and the surface area is 2(pi)r*2(pi)R. Therefore the ratio of volume to surface area is the same as the area of a circle to its circumference: r/2. If this ratio is 3/2, r/2=3/2 and r=3.