Question

1. A Babylonian tablet found in 1936 shows that the Babylonians sometimes used a more accurate value of π than 3. They determined the area of a circle by taking it as equal to of the square of the circle’s circumference. What value of π does this yield? Hint: Set the expression that we use for the area of a circle (πr2) equal to (circumference)2. Solve this equation.

Answer 1

Answer:

1/4

Step-by-step explanation:

Area of a circle is given as πr² and its circumference is expressed as 2πr.

If the babylonians determined the area of a circle by taking it as equal to the square of the circle’s circumference then;

Area of circle = (circumference of a circle)²

πr² = (2πr)²

πr² = 4π²r²

Dividing both sides of the equation by πr² we have;

$\frac{\pi r^{2} }{\pi r^{2} } =\frac{4\pi^{2} r^{2} }{\pi r^{2} }\\1 = 4\pi \\\pi =\frac{1}{4}$

The value of π this yields is 1/4