In this problem, we will look at properties of solids with base on the xy-plane given by the circle x2+y2=a2 and its interior, where a>0
is to be given in parts (i) and (ii) below.
(i). Let a=4, and assume that cross-sections of thesolid perpendicular to the x -axis are circular disks with diameters lying in the xy-plane. Find the area A(x) of the cross-section at location x.
(ii). Let a=9, and assume that cross-sections of the solid perpendicular to the x-axis are equilateral triangles with bases in the xy-plane. Find the area A(x) of the cross-section at location x.
(iii). Find the volume of the solid described in (i) above.