Question

The area of the square base is S(x), where x is the length of the concrete foundation, and the area of the base of the cylindrical tank is C ( r ), r is the radius of the cylindrical tank. What does the expression S ( C ( r ) ) represent?

Answer 1

C(r) is the area of the base of a cylindrical tank with radius r.

We know that this area is:

C(r) = pi*r^2

S(x) is the area of the square base where x is the side length of the base.

S(x) = x*x

Now, we have the expression:

S( C(r)) wich means that we are evaluating the function S(x) in the point x = C(r)

Now, we have a problem here.

In S(x), S(x) is in units of area, and x is in units of length.

And the same for C(r), C(r) is in units of area, and r in units of length.

then we can not have x = C(r)

Then this expression does not represent anything, because the units do not match, so it has no physical sense.