Question

The stiffness of a beam of rectangular cross section is proportional to the breadth and the cube of the depth, If the breadth is 20 cm, express the stiffness as a function of the depth.

Answer 1

Since you said "proportional", I assume you meant directly proportional. In that case, given the information you provided, the relationship should look like this:

S=kbd^3

Where S is the "stiffness", k would be a constant of proportionality, b is the breadth, and d is the depth.

They gave you a value to plug in for b, so that you will have a function of only one variable, d. If you substitute 20 for b, your function becomes:

S = k*20*d^3 , or S = 20kd^3

Also, rather than just showing "S" in the equation, they may instead use this notation, S(d), which means S as a function of d (not S times d - I know that may seem silly to point out, but I have encountered several people who were confused by that notation!).

I hope this was helpful!