SOLUTION: https://media.discordapp.net/attachments/723023718497910816/844368375442178068/unknown.png

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Question 1180627: https://media.discordapp.net/attachments/723023718497910816/844368375442178068/unknown.png
Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Consider the following diagram, depicting one of the cut-off corners with equilateral triangle ABC and "peak" of the pyramid at O.



Each of the triangles AOB, BOC, and COA is an isosceles right triangle with hypotenuse 6cm. That makes OA=OB=OC=3*sqrt(2).

Then the volume of each cut-off corner can be calculated as the volume of a pyramid with base AOB and height OC.

V=%281%2F3%29%28base%29%28height%29

Then of course multiply that by 8 to find the total volume of the cut-off corners.

You should end up with a total volume of 72*sqrt(2).