Calculus Optimization

Question

Eight feet of wire is to be used to form a square and a circle.

(A) Express the sum of the areas of the square and the circle as a function A of a side of the square x.

(B) What is the domain of A? (Enter your answer using interval notation.)

(C) How much wire should be used for the square and how much for the circle in order to enclose the least total area? (Round your answers to two decimal places.)

square:

circle:

Answer 1

C = 8 - 4x

C = 2πr

2πr = 8 - 4x

r = (4 - 2x) / π

A_c = πr²

A_c = (4 - 2x)²

A = x² + (4 - 2x)²