Consider the solid object lying inside both the cylinder x² + y² = 1 and the sphere x² + y² + z² = 4 for z > 0. The density of this object is p (x, y, z) = x² z. Find the total mass of this object.

Find the exact volume of the solid that results when the triangular region with vertices at 0, 0, 6, 0 and 6, 4 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

A rectangular solid has length L=12.6 mm, width W=23.8 mm, and height H=32.5 mm. Find the length of a diagonal AB from the upper left rear vertex to the lower right front vertex. Round the answer to 1 decimal place.