Suppose a solid in the shape of a sphere of radius 2 has mass density at any point equal to the distance of that point from the nearest point on the surface of the sphere. Find the total mass of the solid.
notice that the nearest point on the surface of the sphere is situated along the line connecting the point to the center of the sphere thus without loss of generality assuming that the sphere is centered at (0,0,0) we get
massDesity = 2 - sqrt(x^2 + y^2 + z^2)
in order to find the total mass you have to integrate the above expression over the volume of the sphere (use spherical parametrization)...