The base of a solid is a circle with radius 3. each cross section perpendicular to a fixed diameter of the base is semicircular. if the circle is centered at the origin and the fixed diameter lies on the x-axis, find the cross-section area a(x).

We are given a solid with a base of a circle with a radius of 3 centimeters. Each cross section which is perpendicular to a fixed diameter of the base is semicircular. We need to find the cross-sectional area.

First, calculate the area of the base:

A = pi * r^2
A = pi * 3^2
A = 9 * pi cm^2

Then, to get the cross-sectional area we need to determine the equation of A (x) with respect the cross section perpendicular to the base. From there, substitute the value of the area of the base and solve for the cross-sectional area.