It's Pi Day - Why Pi is Needed to Fill a Pie

DALL·E 2024-03-14 08.30.47 - A celebration scene for Pi Day, featuring a group of people of diverse ages and backgrounds gathered around a lPhoto byAI created by Dall-e

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Pi day is celebrated every March 14th, or 3/14.

Pi is a number that is 3.141592.....

It goes on forever; it is what is called an irrational number.

Photo byTaso KatsionisonUnsplash

Pi is important.

Pi represents the ratio of a circle's circumference to its diameter and is a fundamental constant in mathematics and physics. Pi Day is an annual celebration of mathematics and a day to indulge in pie, playing on the homophonic relationship between "pi" and "pie."

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Photo byHugo AitkenonUnsplash

Without Pi, you would not be able to calculate the amount of filling to put in say, a 9-inch round pie tin.

Area of the Pie Tin

The area \(A\) of a circle is given by the formula \(A = \pi r^2\), where \(r\) is the radius of the circle.

Given a 9-inch diameter for the pie tin, the radius \(r\) is half of that, so \(r = 9 \, \text{inches} / 2 = 4.5 \, \text{inches}\).

Thus, the area \(A\) is calculated as:

\[A = \pi \times (4.5 \, \text{inches})^2 \]

\[A = 3.141592653589793 \times (4.5)^2 \]

\[A \approx 63.62 \, \text{square inches}\]

Volume of the Pie Tin

The volume \(V\) of the pie filling that the tin can hold, assuming the tin has a cylindrical shape, is given by \(V = A \times \text{depth}\), where \(A\) is the area we just calculated, and the depth is the height of the tin.

Assuming an average depth of 1.5 inches for the pie tin, the volume \(V\) can be calculated as:

\[V = 63.62 \, \text{square inches} \times 1.5 \, \text{inches} \]

\[V \approx 95.43 \, \text{cubic inches}\]

These calculations use \(\pi\) to determine the pie tin's area and volume, showing how much area the bottom of the tin covers and how much filling you'd need to fill it to a depth of 1.5 inches completely.

To put it another way

To fill a standard 9-inch pie tin to a depth of 1.5 inches, you would need approximately 6.616 cups of liquid measure.