Question

Find the volume of the solid obtained by rotating the region bounded by the curves x = 2 sqrt(5y), x = 0, and y = 5 about the line x = 0?

Answer 1

To find the volume of the solid obtained by rotating the region bounded by the curves x = 2 sqrt(5y), x = 0, and y = 5 about the line x = 0, we can use the disk method.

Step-by-step explanation:

To find the volume of the solid obtained by rotating the region bounded by the curves x = 2sqrt(5y), x = 0, and y = 5 about the line x = 0, we can use the disk method.

The disk method involves integrating the area of infinitesimally thin disks perpendicular to the axis of rotation. In this case, the axis of rotation is the line x = 0. The radius of each disk is given by the distance from the line x = 0 to the curve x = 2sqrt(5y), which is r = 2sqrt(5y).

The volume can be calculated by evaluating the integral:
V = pi * integral from y = 0 to y = 5 of (r^2) dy
V = pi * integral from y = 0 to y = 5 of (2sqrt(5y))^2 dy