+0  
 
0
5
1
avatar+1002 

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.

 

 Jan 13, 2024
 #1
avatar+36915 
+1

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 

 Jan 13, 2024

2 Online Users