The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 28 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle θ in the figures. (Use k as your proportionality constant.) I have figured that the width is cos(theta)28 and depth is sin(theta)28 squared. What I had come up with is k*cos(theta)28*(sin(theta)28)^2 so if this is right, please let me know.

Question

The strength of a beam is proportional to the width and the square of the depth. A beam is cut from a cylindrical log of diameter d = 28 cm. The figures show different ways this can be done. Express the strength of the beam as a function of the angle θ in the figures. (Use k as your proportionality constant.)  I have figured that the width is cos(theta)28 and depth is sin(theta)28 squared.  What I had come up with is k*cos(theta)28*(sin(theta)28)^2 so if this is right, please let me know.

anonymous · Answer

$$s(\theta)=21952k \cos (\theta)\sin ^{2}(\theta)$$