find the volume of the solid generated by revolving the area by the given curves about the indicated axis of revolution y^2=4ax,x=a;about the y-axis

Answer 1

using shells,
v = ∫[0,a] 2πrh dx
where r = x and h=2y=4√(ax)
v = ∫[0,a] 2πx(4√(ax)) dx = 16/5 πa^3

using discs,
v = ∫[0,2a] π(R^2-r^2) dy
where R=a and r=x=y^2/(4a)
v = ∫[0,a] 2π(a^2-(y^2/(4a))^2) dy = 16/5 πa^3