Final answer:
The question involves using the disk method to find the volume of a solid of revolution, formed by rotating a region bounded by given curves around the y-axis, and it can be solved by setting up and evaluating an integral.
Step-by-step explanation:
The question asks to find the volume V of the solid obtained by rotating the region bounded by the curves y = 1/49x², x = 5, y = 0 about the y-axis. This is an application of the method of solids of revolution, specifically using the disk method. We integrate across the x-axis since we are rotating around the y-axis and the functions are functions of x.
Step-by-step, the solution involves first setting up the integral:
∫ₓ₀⁵ (π (1/49x²)²) dx, which represents the sum of the areas of the infinitesimally thin disks from x = 0 to x = 5. Then, we compute this integral using basic integration techniques. The final volume is found after evaluating the integral.
In the context of the provided information, think of each disk having a cross-sectional area (A) and integrating along the height (x-axis in this case) is similar to finding the average depth (h) in the context of finding volumes of reservoirs.