Find the volume of the solid generated by revolving about the x-axis the region bounded by the upper half of the ellipse (x^2/a^2) + (y^2/b^2) =1 and the x-axis....

Question

Find the volume of the solid generated by revolving about the x-axis the region bounded by the upper half of the ellipse (x^2/a^2) + (y^2/b^2) =1 and the x-axis, and thus find the volume of a prolate spheroid. Here a and b are positive constants, with a>b.

Volume of the solid of revolution?

Answer 1

V = π∫_-a^a(1 - x²/a²)b²dx = 2π(x - x³/3a²)b²₀^a = 4πab²/3