Question
A rectangular beam will be cut from a cylindrical log of radius r =30 inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.
Answers
s = kwd^2
since w^2 + d^2 = 60^2,
d^2 = 3600-w^2
s = kw(3600-w^2)
ds/dw = k(3600-3w^2) = 3k(1200-w^2)
ds/dw = 0 when w=20√3
so d = 20√6
since w^2 + d^2 = 60^2,
d^2 = 3600-w^2
s = kw(3600-w^2)
ds/dw = k(3600-3w^2) = 3k(1200-w^2)
ds/dw = 0 when w=20√3
so d = 20√6