The Area Is The Same

Calculus Level 2

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

  • Solid A is obtained by revolving the blue region, 0y12x 0 \leq y \leq \frac{1}{2} x , about the xx-axis.
  • Solid B is obtained by revolving the red region, 12xyx \frac{1}{2} x \leq y \leq x , about the xx-axis.

Which solid has the greater volume?

Note: aa is a positive real number.

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