3. Let S be the solid formed by rotating the finite area bounded by r = 0, r = 3, y = 0, and y = = 3+2 I+ 1 around the y-axis. In this question, we'll find the volume of S using cylindrical shells. r+2 r+ 1 Figure 3: the region rotated to form S (a) Sketch the portion of the solid resulting from rotating the finite area bounded by r = 1, r = 1.1, y = 0, and y = = +2 r+1 around the y-axis. (b) Use your formula from 2(e) to approximate the volume of the solid in (a)- (c) What is the approximate volume of a cylindrical shell with radius ro, width Arg, and height To + 2. To +1 - ? (Continue to use the formula from 2(e).) (d) We can imagine the solid S consisting of layers of thin cylinders, or cylindrical shells, similar to the shape you found in (a)- r+2 r+ 1 Figure 4: approximationg S using cylinders We want to create a collection of these cylindrical shells that makes up all of S. What are the largest and smallest radii such shells could have? (e) "Adding up" the volumes of all the cylindrical shells will give us the volume of S. Find the volume of S by evaluating [g(x) dr where a and b are the limits found in (d), and g(x) de is adapted from (c)