The Area Is The Same

Calculus Level 3

In the interval $0 \leq x \leq a$ :

Solid A is obtained by revolving the blue region, $0 \leq y \leq \frac{1}{2} x$ , about the $x$ -axis.
Solid B is obtained by revolving the red region, $\frac{1}{2} x \leq y \leq x$ , about the $x$ -axis.

Which solid has the greater volume?

Note: $a$ is a positive real number.