## Circumference If you measure the distance around a circle and divide it by the distance across the circle through its center, you will always come close to a particular value, depending upon the accuracy of your measurement. This value is approximately 3.14159265358979323846... We use the Greek letter (Pi) to represent this value. Using computers, mathematicians have been able to calculate the value of to billions of places.

The distance around a circle is called its circumference. The distance across a circle through its center is called its diameter. Pi ($\large\pi$) is the ratio of the circumference of a circle to its diameter. For any circle, if you divide its circumference by its diameter, you get a value close to $\pi$. This relationship is expressed in the following formula: $\frac{C}{d}\,=\,\pi$, where C is the circumference and D is the diameter. You can test this formula at home with a dinner plate. If you measure the circumference and the diameter of the plate and then divide the circumference by the diameter, your quotient should come close to $\pi$. Another way to write this formula is:

$$\large~C\,=\,\pi\cdot~d$$

 Using $\pi~\,=\,3.14$ Using $\pi~\,=\,3\frac{1}{7}$ Find the circumference of this circle with a diameter of 8 inches. $$\mbox{Use}\,\pi~\,=\,3.14$$ $$C\,=\,\pi~\,\cdot~\,d$$ $$C\,=\,(3.14)\,\cdot~\,(8)$$ $$C\,=\,25.12\,inches$$ Find the circumference of this circle with a diameter of 35 inches. $$\mbox{Use}\,\pi~\,=\,3\frac{1}{7}$$ $$C\,=\,\pi~\,\cdot~\,d$$ $$C\,=\,3\frac{1}{7}\,\cdot~\,35$$ $$C\,=\,\frac{22}{7}\,\cdot~\,\frac{35}{1}$$ $$C\,=\,110\,cm$$ Find the circumference of this circle with a diameter of 8 inches in terms of $\large~\pi$. $$C\,=\,\pi~\,\cdot~\,d$$ $$C\,=\,\pi~\,\cdot~\,(8)$$ $$C\,=\,8\pi~\,inches$$

 Use this applet to observe how to find the circumference of any circle using either 3.14 or $3\frac{1}{7}$ and when given the radius or the diameter. Move the blue and green points to create the circle of your choice. Then use the slider on the left to choose whether the radius or the diameter is given. The slider on the right selects which version of $\pi$ is being used.

# Self-check

Q1: What is the circumference of a circle with a diameter of 10 cm? (Use π = 3.14) [show answer]

Q2: What is the circumference of a circle with a diameter of 14 cm? (Use π = 3 1/7) [show answer]

Q3: In terms of π, what is the circumference of a circle with a diameter of 8 cm? [show answer]