If a beam with a depth of 3.5 inches can support 1000 lbs, how much weight can the same beam hold if it's depth is 12 inches?

Question

The strength of a rectangular wood beam varies directly as the square of a depth of its cross section. If a beam with a depth of 3.5 inches can support 1,000 pounds, how much weight can the same type of beam hold if it's depth is 12 inches?

Answer 1

Let strength = s

Let depth = d

constant of proportion = k

 

Strength varies directly as the square of a depth of its cross section:

s = kd²

 

We use the information given to solve for k

 

1000 = k(3.5²)

1000 = 12.25k

divide both sides by 12.25

 

k = 1000/12.25 = 81.632653

 

Now, using the value found for k, plug in the new information

to solve for the new strength

 

s = 81.632653(12²)

s = 81.632653(144)

s = 11,755.1 pounds

 

To the nearest pound the beam can support 11,755 pounds