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 a shown below Show work please

Answer 1

The artist used
`8.6\ in` more of silver wire

Explanation:

see the attached figure to better understand the problem

step 1

we know that

The Perimeter of the square is equal to

`P=4a`

where

a is the length side of the square

`P=40\ in`

so

`40=4a`

`a=10\ in`

so

Each side of the square has a length of 10 in

step 2

Find the circumference of the circle

The diameter of the circle is equal to the length of the side of the square

The circumference is equal to

`C=\pi D`

we have

`D=10\ in`

substitute

`C=(3.14)(10)=31.4\ in`

step 3

Find the difference

`40\ in-31.4\ in=8.6\ in`