How to find the volume of a solid rotated around the y-axis?
Answer: The volume of a solid rotated about the y-axis can be calculated by V = π∫dc[f(y)]2dy.
Let us go through the explanation to understand better.
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 ∫dc [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 ∫dc [f(y)]2dy.