Calculus of variations: find $y(a/2)$ if $y(x)$ maximizes the volume of rotation

Question

A curve $y(x)$ of length $2a$ is drawn between the points (0,0) and (a,0) in such a way that the solid obtained by rotating the curve about the $x$-axis has the largest possible volume. Find $y\left(\frac{a}{2}\right)$.