bonanova Posted January 9, 2009 Report Share Posted January 9, 2009 Someone gave you a plank of wood with holes shaped as a triangle, square and circle of the indicated dimensions. Also, a 2"x2"x2" cube of wood. Can you make a single shape from that cube that will pass through each hole and completely fill it? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted January 9, 2009 Report Share Posted January 9, 2009 Someone gave you a plank of wood with holes shaped as a triangle, square and circle of the indicated dimensions. Also, a 2"x2"x2" cube of wood. Can you make a single shape from that cube that will pass through each hole and completely fill it? The original cube fits and fills the square hole. If you lathe it along one axis to a cylinder with a 2" diameter, it will also fit the circular hole. [looking from the top it will be a circle, and from the side a square.] If you then view it from the side, and lop off sections from the top center of the top (circle) to the edges of the bottom you'll have the equilateral triangle Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted January 9, 2009 Author Report Share Posted January 9, 2009 The original cube fits and fills the square hole. If you lathe it along one axis to a cylinder with a 2" diameter, it will also fit the circular hole. [looking from the top it will be a circle, and from the side a square.] If you then view it from the side, and lop off sections from the top center of the top (circle) to the edges of the bottom you'll have the equilateral triangle Why do I do the effort of photoshopping these things when in 2 seconds they're solved? Nice one! Quote Link to comment Share on other sites More sharing options...
0 Prof. Templeton Posted January 9, 2009 Report Share Posted January 9, 2009 I was going to post my answer, but i got beat (again), so I made a drawing instead Start in the top center of a cylinder and cut two planes down at an angle to the bottom edge of the cylinder. View we see here is a square, rotate 90 either left or right for a triangle and the bottom is still the bottom of the cylinder so it's a circle. Quote Link to comment Share on other sites More sharing options...
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bonanova
Someone gave you a plank of wood with holes shaped as a triangle, square and circle of the indicated dimensions.
Also, a 2"x2"x2" cube of wood.
Can you make a single shape from that cube that will pass through each hole and completely fill it?
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