# 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.

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