3. (a) Use double integral to find the volume of the solid bounded by the cylinder

x

2 + y

2 = 16 and the planes z = 0, z = 5 y.

(b) Suppose that the pressure of a fluid body at a point (x, y) on a flat plate is given

by P(x, y) = 5 4x

2 y

2

. Find the average pressure of the rectangular portion of

the plate for which 0 x 2 and 0 y 1.