Question

In ancient egypt, a scribe equated the area of a circle with a diameter of 9 units to the area of a square with a side length of 8 units. what value of pi does this method produce

Answer 1

`\pi =3.160494`

Explanation:

step 1

Find the area of the circle with a diameter of 9 units

we know that

The area of a circle is equal to

`A=\pi r^(2)`

we have

`r=9/2=4.5\ units` ----> the radius is half the diameter

substitute

`A=\pi (4.5)^(2)`

`A=20.25\pi\ units^2`

step 2

Find the area of a square with a side length of 8 units

we know that

The area of the square is

`A=b^2`

where

b is the length side of the square

we have

`b=8\ units`

substitute

`A=(8)^2=64\ units^2`

step 3

Equate the areas

`20.25\pi=64`

solve for
`\pi`

`\pi =(64)/(20.25)=3.160494`