4.

(a) Prove that the volume bounded by the ellipsoid is 47rabc/3.

(b) Let

a, b,

c, d be positive numbers and r2 < d2/(b2 + c2). Find the volume of the region bounded by y2 + Z2 = r2, x = 0, and ax + by + cz = d.

(c) Show that for any a 2: 0, the volume of the region bounded by the cylinders x2 + Z2 = a2 and y2 + Z2 = a2 is 16a3 /3.