For the solid s described, do the following:

(a) sketch the base of s in the xy-plane.
(b) sketch a three-dimensional picture of s with the xy-plane as the floor.
(c) compute the volume of s.

1. the base of s is the region lying above the parabola y = x 2 and below the line y = 1 over the interval 0 ≤ x ≤ 1. cross-sections perpendicular to the x-axis are square

(a) and (b) see pictures attached

(c) V = 16/35

Step-by-step explanation:

(a) Sketch the base of S in the xy-plane.

See picture 1 attached

(b) Sketch a three-dimensional picture of S with the xy-plane as the floor.

See picture 2 attached

(c) Compute the volume of S.

The volume is given by the triple integral

The cross-sections perpendicular to the x-axis are squares so  

The region S is given by the following inequalities

Therefore

So the volume V of the solid S is

V=16/35

step-by-step explanation:

x^2 -12x + 36 + y^2 = 36

x^2 + y^2 = 12x

r^2 = 12rcos(theta)

r = 12 cos(theta)