A journey back to three dimensions this week.
You have a cube. The surface area of the cube is 150 cm^2. A "cross
section" of the cube is a shape that you get when you cut the cube with a
plane - sort of like slicing it. If you cut the cube with a plane that is
parallel to one of its faces, you will get a square.
Questions: What would be the perimeter of that square? What is the
perimeter of the largest rectangle you can get as a cross section? Can
you figure out how to get an equilateral triangle as a cross section?
Extra: What's the area of the square? the rectangle? the biggest
possible equilateral triangle?
To make explaining this easier, I've provided a labelled cube below. ABCD
is the front of the cube, while EFGH is the back. Be sure to explain your
answers so that someone else might learn something from reading your
solution.
