This problem is a variation on a problem from that GRE preparation book I used last week, slightly altered because the way they worded this problem was too easy.A 'cross section' of a cube is a shape that you get when you cut the cube with a plane - sort of like slicing it.
You have a cube with a surface area of 96 cm^2 (that's 96 square centimeters). 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.
- Annie Fetter
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