<p>Ok... I guarantee you it is 1/8 and not 1/6... Here are 2 ways to solve it.</p>
<p>Lets call the side length of the cube s.... The triangle piece thus has the top dimensions 1/2s x 1/2s x s and a volume of (1/2)(1/2s)(1/2s)(s)=1/8s^3. The cube has a volume of s^3. Take the ratio to get 1/8.</p>
<p>Another way to solve it is to take each midpoint of one face of the cube and connect them. What you will get is 8 equal triangles. Each of these triangles represents one of those slices, so it is 1/8.</p>
<p>It isn't 1/6. I heard some people say if you divide the center cube down the middle you have 2 of the identical triangle pieces... That is wrong. The center triangles have the dimensions sqrt(2)s/2 x sqrt(2)s/2 x s.</p>
<p>its 1/8. think about it. the surface area of the cube on the top (the triangle formed) is 1/8 the surface area of the top cube. thats all u need to know.</p>
<p>LOL NICE i put 1/8 and then my friend told me it was 1/6 for sure at the break and i was like dang.. i should change it but i was like ***NO ima trust myself and i left it</p>
<p>lol, albert, I love how direct you are - but it's a good idea; I find it hard to see how anyone would think that it's 1/6 (that triangle thing they mention doesn't make any sense). All that's necessary is multiplying 1/2<em>1/2</em>1/2 (the triangle base as a proportion of the entire base), since the height is the same for both.</p>