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Today's calculation of Integral 566

Source: 2010 Kyoto University entrance exam/Science #6, Humanities #5

February 26, 2010
calculusintegrationanalytic geometrygeometry3D geometryrotationsymmetry

Problem Statement

In the coordinate space, consider the cubic with vertices O(0, 0, 0), A(1, 0, 0), B(1, 1, 0), C(0, 1, 0), D(0, 0, 1), E(1, 0, 1), F(1, 1, 1), G(0, 1, 1) O(0,\ 0,\ 0),\ A(1,\ 0,\ 0),\ B(1,\ 1,\ 0),\ C(0,\ 1,\ 0),\ D(0,\ 0,\ 1),\ E(1,\ 0,\ 1),\ F(1,\ 1,\ 1),\ G(0,\ 1,\ 1). Find the volume of the solid generated by revolution of the cubic around the diagonal OF OF as the axis of rotation.
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