calculus

The volume of the solid is given by the formula V = ∫2πy[(x-a)^2] dx, where a is the distance from the y-axis to the line of revolution. In this case, a = 6. So, V = ∫2πy[(x-6)^2] dx. Using the limits of integration given by the equations, we can solve the integral and arrive at the volume: V = ∫2π(6-x)(x-6)^2 dx = ∫2π[6x^2-18x+36] dx = [2π*x^3/3 - 3πx^2 + 18πx]|^5_0 = [2π*125/3 - 3π*25 + 18π*5] = 625π - 75π + 90π = 740π So, the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line x = 6 is 740π cubic units.