SOLUTION: Is there a way, just using geometry (i.e. straight-edge & dividers) to find a square whose area is equal to the volume of a given cube?

Question 480200: Is there a way, just using geometry (i.e. straight-edge & dividers) to find a square whose area is equal to the volume of a given cube?
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
You can't compare a two-dimensional quantity with a three-dimensional quantity. In other words, you can't say "the area of the square is greater than the volume of the cube."

You can numerically compare them, but that would be meaningless because the units are relevant. For example, a square with side length 8 cm and a cube with edge length 4 cm numerically have the same area/volume. However, a square with side length .08 m and a cube with edge length .04 m do not.
RELATED QUESTIONS
How do you find the area of a square whose diagonal is equal to... (answered by nerdybill)

Hello, I'm here because I need help doing a proof for my geometry class. I need to prove... (answered by richard1234)

Find the maximum volume of a truncated right prism with regular triangle as base whose... (answered by ikleyn)

I have a square that is inscribed into a circle. The area of the square is 64 square... (answered by Theo)

the topic says measuring segments there a line segment with the point G, H, I... (answered by stanbon)

Find the volume of a cube whose edge is... (answered by Alan3354)

find the volume of earth dug out from a cubical pit whose edge is 2.4... (answered by rfer)

Find the volume of a regular octagonal pyramid whose basal edge is 12dm and altitude... (answered by addingup)

The volume of a cylinder whose height equal to x � 3, is modeled by the polynomial... (answered by Boreal)