Find the mass of the solid hemisphere of radius 1 above the xy-plane with density p(x,y,z) = (z^2)(x^2+y^2+z^2)^1/2

Let B be the solid bounded by the surfaces z=3x^2+4y^2,   x^2+y^2=25, and the xy-plane (distances in cm). Suppose B has a constant mass density of 4 g/cm^3. Here, you will compute the moment of inertia of B about the axis through (−3,4,−4) that is perpendicular to the yz-plane. (a) What is the square of the distance between an arbitrary point (x,y,z) and the axis? r^2=  (b) Find the moment of inertia of B about the axis. Include units on your answer. I=

The center of mass of a lamina of total mass 5 has coordinates (2, 1). What are the lamina’s x- and y-moments?

Find the surface area of part of the paraboloid z = f(x, y) = x^2 + y^2 that lies under the plane z = 4