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

Answer:

$\pi =3.160494$

Step-by-step 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 $\pi$

$\pi =\frac{64}{20.25}=3.160494$