Is this problem even correct? First of all I would think that depth is the dimension that goes inside the log; then ifThe strength of a rectangular beam is proportional to the product of its width w times the square of its depth d. Find the dimensions of the strongest beam that can be cut from a cylindrical log of radius r

Answers: $w=\dfrac{2r}{\sqrt{3}}, h=\dfrac{2\sqrt{2}r}{\sqrt{3}}$depth^2timeswidth=strengththen since depth isn't bounded by anything then it follows that I should just take the biggest possible width.

And if the depth is this vertical side of the beam as shown in the picture, then why does the answer they give is in terms of w and h? What is h (height I assume?) then? Is it the dimension that "goes inside" the log? But then it isn't bounded by anything, so I can make it arbitrarily big and it wouldn't matter.

Can someone clear this up?