Question 537577: Inside a rectangular box, two identical spheres of radius r are tangent to each other and each touches five of the six sides of the box. What is the volume of the box in terms of r?
a)(4/3)r^3
b)(8/3)r^2
c)4r^3
d)8r^3
e)16r^3
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! I assume that the spheres are touching the bottom of the box and what I would call "all four sides." They do not tell me about a sixth side, which would be the lid. I assume that if I put a flat transparent lid on top I would see that the spheres touch the lid too. Otherwise, if the box can be as deep as you wish, with those balls at the bottom, there is no way to know the volume. So, in the solvable version of this problem, the spheres touch all six sides of the box, or would touch if the lid was on.
The box has to be long enough to contain two touching spheres so length=4r.
The other two dimensions have to be width=depth=2r to fit one sphere.
The volume of the inside of the box is
Volume = (4r)(2r)(2r)=16r^3
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