13. Let a 2 0. (a) [2 marks] For this part of the question only, select a specific a 2 0, and draw a large sketch of the curve y = 1" on the domain [0, 1] below, indicating your particular choice of a clearly. (b) [4 marks] Let A be the area under the curve y = 2" from r = 0 to z = 1. Find, as a function of a, the volume of the solid obtained by rotating A about the r-axis. 5 (c) [4 marks] Again, let A be the area under the curve y = 2" from 1 = 0 to r = 1. Find, as a function of a, the volume of the solid obtained by rotating A about the y/-axis. (d) [3 marks] Find the constant a 2 0 such that the solids described in parts (b) and (c) have the same volume. Explain, without using calculus, why that choice of constant yields two shapes of the same volume