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bonanova
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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.

post-1048-1231526175.gif

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

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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? :o

Nice one! ;)

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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.

post-9402-1231529927.jpg

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