PI

Returns 3.14159265358979, the value of the mathematical constant PI to 14 decimal places.

Syntax:

PI()

Example:

PI()

returns 3.14159265358979

Application:

The Goal: A farmer wants to build a circular fence to enclose a new, circular garden. The farmer has 100 meters of fencing material. She needs to know how wide the garden will be to plan the planting layout.

The Math:

The formula for the circumference (C) of a circle isC=π⋅d, whered is the diameter.

In this case, the total length of the fencing material is the circumference of the circle.

C=100 meters
We need to find the diameter (d).
So, we rearrange the formula to solve ford:d=C/π

Calculation:

d=100/π≈100/3.14159 d≈31.83 meters

The farmer now knows that her circular garden will have a diameter of approximately 31.83 meters.

The Table:

This table illustrates the relationship between the diameter, circumference, and area of a circle, using π in the calculations. Imagine the farmer is considering different-sized gardens with the same fencing material.

Fomulas Used:

C = π⋅d
A = π⋅r2

	Diameter (d)	Circumference (C)	Area (A)
	A	B	C
1	10 meters	C=π×10=31.42 meters	78.54 m$^2$
2	20 meters	C=π×20=62.83 meters	314.16 m$^2$
3	31.83 meters	C=π×31.83=100 meters	795.77 m$^2$
4	40 meters	C=π×40=125.66 meters	1256.64 m$^2$

This simple example shows how π is an essential constant for calculating the dimensions of circular objects in the real world, whether it's for gardening, engineering, or even calculating the volume of cylindrical tanks.