SOLUTION: The length of the side of a cubical box is 12cm. What is the volume (in terms of x) of the largest ball than can be placed in it?

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Question 808178: The length of the side of a cubical box is 12cm. What is the volume (in terms of x) of the largest ball than can be placed in it?
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
ooh this sounds fun
volume of the cube box is L%2AW%2AH=V
SINCE ITS A CUBE ALL SIDES ARE THE SAME L%5E3=V IF L=12 THEN V=1728
BUT YOU DON'T WANT THE VOLUME OF THE BOX BUT OF THE BIGGEST BALL THAT CAN FIT INSIDE INSIDE
WE NEED THE VOLUME OF A SPHERE WITH A RADIUS OF 6CM
VOLUME OF A SPHERE: %284%2F3%29%28pi%29%28r%5E3%29
r=6
%284%2F3%29%28pi%29%286%5E3%29=x
%284%2F3%29%28pi%29%28216%29=x
4%2872%29%28pi%29=x
288%28pi%29=x
904.7786842338604526772412943845=x
now depending on how thick the sides of the boxes are will decrease this maximum value of this box. technically it is a tad bit less then the above number so rounding down would be sufficient at 904.7786=x
hope this helps