Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis. y = 0, y = x(8-x) about the axis x = 0

Answer 1

By shell method: v =2π∫₀⁸x·x(8 - x)dx = 2π(8x³/3 - x⁴/4)₀⁸ = 2π·8³(8/3 - 8/4) = 2048π/3