Final answer:
To find the volume of the solid obtained by rotating the region bounded by the curves x = 4p3y, x = 0, and y = 3 about the y-axis, we can use the method of cylindrical shells. The formula for the volume of a solid obtained by rotating a bounded region about the y-axis is given by V = 2π∫(x)(y)dx. We need to express x in terms of y and determine the limits of integration.
Step-by-step explanation:
Volume of Solid Obtained by Rotating the Bounded Region
To find the volume of the solid obtained by rotating the region bounded by the curves x = 4p3y, x = 0, and y = 3 about the y-axis, we can use the method of cylindrical shells. The formula for the volume of a solid obtained by rotating a bounded region about the y-axis is given by V = 2π∫(x)(y)dx. We need to express x in terms of y and determine the limits of integration.
Step-by-step Solution:
- Express x in terms of y: x = 4p3y
- Determine the limits of integration: y = 0 to y = 3
- Calculate the expression for the volume: V = 2π∫(x)(y)dx
- Integrate the expression over the given limits
After performing the integration, you will find the volume of the solid obtained by rotating the region about the y-axis.