Cavalieri's Principle and Volume of Composite Figures

Question 2 • Fall 24 GMS Geometry: Concepts and Connections B

The cross-sectional area of the shaded circle is πx2. Using the Pythagorean theorem for the right triangle, we get x2 + b2 = r2. Now solve for x2 and substitute it into the area expression.What is the result?

Answer

π(r2 – b2)

π(r2 + b2)

π(b2 – r2)

2π(b2 + r2)

Explanation

From x² + b² = r², subtract b² from both sides to get x² = r² − b². Substitute this into the area formula πx²: the area is π(r² − b²), which is choice A.

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