2. Solve for indicated areas and volumes respective to given objects

a) FInd the area of the cardioid r = 8 + 8sin(Theta)

b) Find the volume of the solid over the xy-plane and under the FIRST OCTANT portion of the surface z = 25-x², 1<=y<=8

c) vind the volume of the region common to the cylinders x²+z²=16 and y²+z²=16

d) Consider the cylinder x²+y²=36 and the sphere x²+y²+z²=100. Find the volume OUTSIDE the cylinder and INSIDE the sphere.

e) FInd the volume of the region inside the one-sheeted hyperboloid x²+y²-z²=36 between z= -8 and z= 8

f) Consider the "ice cream cone" formed by the upper half of the sphere x²+y²+z²=400 and the cone z=3x2+3y2. Find the z-coordinate of its center of mass written as a rounded decimal number with at least three decimal places after the decimal, assuming the density is constant.