A Cavalieri Comparison

Problem

Let $V_1$ be the volume of the solid obtained by rotating the region bounded by

x^2 = 4y, \quad x^2 = -4y, \quad x = 4, \quad x = -4

about the $y$ -axis, and $V_2$ the volume of the solid obtained by rotating the region

x^2 + y^2 \leqslant 16, \qquad x^2 + (y-2)^2 \geqslant 4, \qquad x^2 + (y+2)^2 \geqslant 4

about the $y$ -axis. Find $\dfrac{V_1}{V_2}$ .

Answer

Solution

Difficulty	8/10
Topics	calculus, solid geometry, Symmetry

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