Thread: Rectangular Wooden Beam

The strength of a rectangular wooden beam is proportional to the product of the width and the cube if its depth. If the beam is to be cut from a log in the shape of a cylinder of radius 3 feet, express the strength S of the beam as a function of the width x. Also, what is the domain of S?

Originally Posted by symmetry

The strength of a rectangular wooden beam is proportional to the product of the width and the cube if its depth. If the beam is to be cut from a log in the shape of a cylinder of radius 3 feet, express the strength S of the beam as a function of the width x. Also, what is the domain of S?

Hello,

I've attached a rough sketch of the situation.

According to the problem



From the diagram you know:



Now plug in the term for d into the equation with S:

.

To get real results it is necessary that the radicand is equal or greater than zero. Thus the value of x must be greater than zero and smaller than 2r:



EB

Great reply as always but how do you make such diagrams?

You said:

"Now plug in the term for d into the equation with S."

What exactly do you mean by this statement?

Originally Posted by symmetry

You said:

"Now plug in the term for d into the equation with S."

What exactly do you mean by this statement?

Hello,

from my previous post:



Now I took the RHS of this equation which contains the term for d and put it into the equation for S:






EB

I finally get it.

Thanks!