566

Part of 2010 Today's Calculation Of Integral

Problems(1)

Today's calculation of Integral 566

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

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)

. Find the volume of the solid generated by revolution of the cubic around the diagonal

OF

as the axis of rotation.

calculusintegrationanalytic geometrygeometry3D geometryrotationsymmetry