Question

An artist used silver wire to make a square that has a perimeter of 40 inches. She then used copper wire to make the largest circle that could fit in the square, as shown below.

What is the area of the copper circle? Use 3.14 to represent π.

Answer 1

The area of the copper circle A= 69.08
`inches^(2)`.

Explanation:

Given data,

Perimeter of the Square =40 inches.

Let us find the measurement of one side.

The formula for perimeter of a square is 4a.

where a is length of one side of a square.

We know that perimeter of the square is 40.

∴ 4a=40.

a=10 inches.

Imagine that moving one side of the square into the circle.

You can observe that length of one side of square is the diameter of the circle.

∴Diameter of the circle =10 inches.

⇒ Radius of the circle r= 5 inches.

Area of the circle A= π
`r^(2)`.

A= 3.14×5×5.

Area of the circle A= 69.08
`inches^(2)`.