Final answer:
To find the volume of the solid obtained by rotating the region bounded by y = 8x + 40, y = 0, x = 0 about the y-axis, use the method of cylindrical shells and integrate the function.
Step-by-step explanation:
To find the volume of the solid obtained by rotating the region bounded by y = 8x + 40, y = 0, x = 0 about the y-axis, we can use the method of cylindrical shells.
The volume of the solid is given by the integral V = ∫[a, b] (2πx)(8x + 40) dx.
Simplifying that integral gives V = 16π∫[a, b] (x^2 + 5x) dx.
Integrating the function gives V = 16π[x^3/3 + (5/2)x^2], evaluated from x = 0 to x = b.
Substituting the given values into the equation and evaluating the integral gives the desired volume: Volume = (136π/3) cubic units.