How to find the volume of a solid rotated around the y-axis?

Other than the disk method, we can also use the washer method for finding the volume of rotated solids.

Answer: The volume of a solid rotated about the y-axis can be calculated by V = π∫^d_c[f(y)]²dy.

Let us go through the explanation to understand better.

Explanation:

The volume of a solid rotated around the y-axis can be calculated using the "Disk Method"

The disk method is predominantly used when we rotate any particular curve around the x or y-axis.

Suppose a function x = f(y), which is rotated about the y-axis.

The volume of the solid formed by revolving the region bounded by the curve x = f(y) and the y-axis between y = c and y = d about the y-axis is given by

V = π ∫^d_c [f(y)]²dy.

The cross-section perpendicular to the axis of revolution has the form of a disk of radius R = f(y).

Thus, the volume of a solid rotated about the y-axis is calculated to be V = π ∫^d_c [f(y)]²dy.