Consider the solid torus (the donut-shaped solid shown in the figure) with radii 7r and 2R. a = 2 b = 7 aR br) (a) Set up an integral for the volume of the given solid. 7r 16-R " V49,2 – y?dy -7r 16т R V49r2 – r?dr -7r 7r 87 R xdr 7r / (49,² – y²)² dy 167 R 7r 87 R ydy -7r (b) By interpreting the integral as an area, find the volume V of the torus. V =

The integral represents the volume of a solid. Describe the solid. √3 2π(7-y)(3- y²) dy The solid is obtained by rotating the region bounded by (i) x = 3-y² X , x = 3, and y = 0 about the line y = 7 v , x = 0, and y = 0 or (ii) x = using cylindrical shells.