+1439 Donatello starts with a marble cube. He then slices a pyramid off each corner, so that in the resulting polyhedron, all the edges have the same side length. If the side length of the original cube is $6$, then find the volume of the resulting polyhedron.
+37146 Original volume = 6 x 6 x 6 = 216 in^3
Now remove three triangular pyramids with side length 2 inches
slant height 2 inches translates to height sqrt 5 and area of 1/2 * 2 * sqrt 5 = sqrt 5 in^2
for a volume 1/ 3 (base ) (height) = 1/3 ( sqrt 5)(sqrt 5 ) = 5/3 in^3
eight of these then subtract 40 / 3 in^3 from the original volume= for a final volume 202 2/3 in^3
