Find the composition A ° r and explain what it represents in the context of the problem.

Question

A square concrete foundation was prepared as a base for a cylindrical propane tank.
a. express the radius,r,of the tank as a function of the length, x, of the sides of the square.

b. express the area, A, of the circular base of the tank as a function of the radius r.

c. Find the composition A ° r and explain what it represents in the context of the problem.

Answer 1

The circle of the base of the tank is inscribed in the square, which means that the diameter of the circle is equal to the side of the square, which means that the radius r = x/2

 

The area of a circle is A = pi*r² 

 

The composition A ° r = A(r(x)) = A(x/2) = pi*(x/2)² = (pi/4)*x² is the area of the base of the tank as a function of a side of the square foundation