Question: Take a unit cube in three dimensions. Cut the cube by a plane perpendicular to the line from its corners (0, 0, 0) and 1, 1, 1), that cuts this line at the point (t/3,t/3, t/3).
a) What is the cross-sectional area of this slice through the cube?
b) Check your answer by describing geometrically the shape of the cross section in the case when t 1 and t = 3/2.