7.2 Finding Volume using the Washer Method, Study notes of Analytical Geometry and Calculus

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7.2 Finding Volume using the Washer Method

Example 1) Find the volume of the solid formed by revolving the region bounded by the graphs y = √x and y = x^2 about the x-axis.

This application of the method of slicing is called the washer method.

The shape of the slice is a circle with a hole in it, so we subtract the

area of the inner circle from the area of the outer circle.

Washer Method Formula

OR

Example 3) Find the volume of the region bounded by the

curves y = x and y = x

2

when it is rotated about the line y = 3.

If we use a horizontal slice, the disk now has a hole in it, making it a washer. The volume of the washer is: outer radius inner radius thickness Example 4) The region bounded by y = x^2 and y = 2x is revolved about the y-axis. Find the volume.

Example 7) Find the volume of the region bounded between x = 0, y = 1, x = 1, y = (x-1)^2 +1 when it is rotated.... a) about the x-axis b) about x = - c) about x = 2