# Problem of the day

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.

lwh+2lw+2hw+2lh+h(pi)+l(pi)+w(pi)

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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:

$$L W H+2L W+2H W+2L H+\pi H+\pi L+\pi W + \frac{4}{3}\pi$$

saltydog