Consider the top half of a solid sphere of radius 5, i.e. x² + y² + z² ≤ 25 for z ≥ 0. If the density of this hemisphere is given by p (x, y, z) = √x² + y² + z², use spherical coordinates to find both the total mass m and the z-coordinate of the center of mass of the hemisphere.

Find the exact volume of the solid that results when the triangular region with vertices at 0, 0, 5, 0 and 0, 9 is rotated about the a x-axis b y-axis

Find the exact lateral area of each solid in Exercise 40. Find the exact volume of the solid formed when the region bounded in Quadrant I by the axes and the lines x = 9 and y = 5 is revolved about the a) x-axis b) y-axis

Sketch the solid that results when the given circle of radius length 1 unit is revolved about the horizontal line that lies 1 unit below the center of that circle.