The strenght of a rectangular beam is proportion to its width (w) and its square thickness (t) that is S=kwt^2, where k is a constant. Find the dimensions of the strongest beam that can be cut from a cylindrical log of radius 20cm.

Question

anonymous · Answer

It's been a long time since we reviewed optimization, so I might be wrong....

Solve for S'=0 to get the max strength
and use this:
(w^2+t^2)/2=r

anonymous · Answer

that should be w^2 + t^2 = (2r)^2 right?

anonymous · Answer

thank you for replyin but where did you get the (w^2+t^2)/2=r from?
I understand to find the max strength we set s' to zero, but the second part you mentioned confused me o.0

anonymous · Answer

i dont think what he gave you is correct. draw a cross-section of the beam, a circle, a square inscribed in the circle, so the sides of the rectangle should be the width and thickness, and the diagonal of the rectangle is the diameter

anonymous · Answer

Yeah my bad. sorry.
half the diagonal of a enclosed rectangle is the radius of the outside circle is what I was aiming for.

anonymous · Answer

hey INT are you sure you got that series question?

anonymous · Answer

okay no i understand, thank you guys so much!!

anonymous · Answer

*now