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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