The Area Is The Same

Calculus Level 2

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.