Find the volume V of the solid obtained by rotating the region bounded by the given curves about the specified line.

Question

x = 2 sqrt.(5y) x= 0, y = 3

Answer 1

We have that y ≥ 0 and x ≥ 0. So x² = 20y, y = x²/20. x-coordinate of point of intersection x²/20 = 3, x² = 60;

x = 2√15. If y = 3 axis of revolution, then V = π∫₀^2√15(3² - (x²/20)²)dx = π∫₀^2√15(9 - x⁴/400)dx =

π(9x - x⁵/2000)₀^2√15 = π(18√15 - 32·225√15/2000) = 14.4π√15 ≈ 175.21