How can the volume of a sphere be determined? (Without simply using a formula you've been told.)

First, let's look at a circular cylinder.The volume is:

Example: Find the volume of the solid obtained by rotating about the x-axis the region under the curve y = √x from 0 to 1.

Any function that is rotated about the x-axis (or y-axis) creates a solid of revolution.

The general formula for finding the volume of a solid of revolution is:

Volume - solids of revolution

Calculus 2 Page 1

region under the curve y = √x from 0 to 1.

Exercises: Find the volume of the solid obtained by rotating the region bounded by the given curve and x-axis. Include a sketch of the solid.1. y = x2 on [0, 1] 2. x + y = 1, x = 0, y = 0 3. y = √x - 1 on [1, 4]

Calculus 2 Page 2