Problem of the day

  • Thread starter Yoda13
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  • #1
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Let B be a solid box with length L, width W, and height H. Let S be the set of all points that are a distance at most 1 from some point of B. Express the volume of S in terms of L,W, and H. Have fun.
 

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  • #2
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lwh+2lw+2hw+2lh+h(pi)+l(pi)+w(pi)
 
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  • #3
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Don't forget the corners: pasted together they constitute a unit-sphere, so there is an extra contribution of 4/3 pi to the volume of S:

[tex]L W H+2L W+2H W+2L H+\pi H+\pi L+\pi W + \frac{4}{3}\pi[/tex]
 
  • #4
saltydog
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Ok thanks. Now I know what you guys were talking about. I though he meant a point INSIDE the box say (h,j,k). I think that's a little more difficult: what is the volume of the solid formed by all points inside the box that are a distance of 1 unit away from the point (say for a box 2x2x2)? Are there points in the box that yield a miniumum volume? Is it at the corners? So conceivably, we could construct a function of 3 variables: f(x,y,z), which yields this volume as a function of position in the box. Really, I think just calculating one such volume would be difficult.
 
  • #5
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o right, i forgot about the corners, thanks
 
  • #6
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can someone please explain where the l(pi)+h(pi)+w(pi) came from. sorry im a physics student and we were given a similar problem, and i just dont really understand. our was for a different shape and different distance but i think this helps.
 

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