Exploring Circumference

Student Summary

There is a proportional relationship between the diameter and circumference of any circle. That means that if we write CC for circumference and dd for diameter, we know that C=kdC=kd, where kk is the constant of proportionality.

The exact value for the constant of proportionality is called pi, and its symbol is π\boldsymbol\pi. Some frequently used approximations for π\pi are 227\frac{22} 7, 3.14, and 3.14159, but none of these is exactly π\pi.

A graph of a line in the coordinate plane with the origin labeled O.
A graph of a line in the coordinate plane with the origin labeled O. The horizontal axis is labeled “d” and the numbers 1 through 6 are indicated. The vertical axis is labeled “C” and the numbers 2 through 12, in increments of 2, are indicated. The line begins at the origin, slants upward and to the right, and passes through the point 1 comma pi.

We can use this to estimate the circumference if we know the diameter, and vice versa. For example, using 3.1 as an approximation for π\pi, if a circle has a diameter of 4 cm, then the circumference is about (3.1)4=12.4(3.1)\boldcdot 4 = 12.4, or 12.4 cm.

The relationship between the circumference and the diameter can be written as

C=πd\displaystyle C = \pi d

Visual / Anchor Chart

Standards

Building On
2.MD.A

2.MD.A

6.SP.5.c

6.SP.B.5.c

Addressing
7.G.4

7.G.B.4

7.RP.2.a

7.RP.A.2.a

7.G.4

7.G.B.4

7.RP.2

7.RP.A.2

Building Toward
7.G.4

7.G.B.4