If I had a cube with a side three feet in length what would be the volume, in cubic feet, for the smallest sphere which could completely encompass the cube?

stuthehistoryguy

((3*sqrt(3)/2)^3)*(4/3)*pi Apr 16 08, 1:05 PM

triviapaul

This is not much of a trivia question, but I'll try to calculate it anyway. I get 27/2*pi*sqrt3 which is about 73,5 cubic feet Apr 16 08, 1:06 PM

sequoianoir

I concur - 73.458874251485822949060169434507 Four thirds Pi x radius cubed where radius is half the square root of 27 Apr 16 08, 1:29 PM

stuthehistoryguy

If you plug the above into Excel (with 3.14 as pi) you get 73.42163373. So, yeah. Apr 16 08, 1:30 PM

rxbigdawg

Actually they came up with the same answer I did, though by a different way. I'm a hack at math so I first found the diameter of the circle by finding the legnth of the diagonal runing from one corner of the cube to the other. Using pythagorian theorum twice first to get the hypotenuse of one of the cubes sides and then to get the hypotenuse of the triangle with one side and the hypotenuse of the face. Thus I found: sqrt(3sq + 3sq) = 4.24 sqrt(3sq + 4.24sq) = 5.196 the diameter of the sphere. 4/3(pi*r^3) is the area of a sphere. Which gives you about 73.58 cubic feet. Apr 16 08, 2:20 PM