Eight cake pieces from only three cuts

Question

You need to divide a round cake into 8 pieces, but you're only allowed 3 straight cuts. With three straight cuts made from directly above (like slicing a pizza), you can get at most 6 or 7 pieces, not 8. How can you make three straight cuts and get exactly 8 pieces?

Accepted Answer

Use the third dimension: cakes are solid, not flat. The three cuts. 1. Cut 1: a vertical cut straight down through the center → 2 pieces. 2. Cut 2: another vertical cut straight down through the center, at a right angle to the first → 4 equal wedges (like quartering a pizza). 3. Cut 3: now cut horizontally, a single slice parallel to the tabletop, halfway up the height of the cake. This one cut splits every wedge into a top half and a bottom half at once. After the horizontal cut, each of the 4 wedges becomes 2 pieces (an upper and a lower), giving 4 	imes 2 = \mathbf{8} equal pieces. Why th…

Eight cake pieces from only three cuts

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