Intro to Circles

A circle is one of the most commonly used geometric shapes in practical and technical work. 

What is a circle? Watch the video below to gain some insight into what a circle is and what a circle isn't.

Once you understand that a circle is the set of points on a flat surface (a plane) that are all the same distance from a given point (the center), you can begin to think about and work with the parts and properties of a circle. The diagram below shows some of the parts of circles that are commonly used. 

The radius of a circle is a line segment from its center to any point on the circle. More than one radius are called radii.
A chord of a circle is a line segment joining any two points on a circle.
A diameter of a circle is a chord that goes through its center. The length of a diameter is twice the length of a radius.

11-1 What are the lengths of the both the radius and diameter of each of the following circles?

a.  

radius = 

diameter =

b.  

radius = 

diameter =

c.  

radius = 

diameter =

11-2 The circumference of a circle is similar to the perimeter for other shapes; it is the length around the circle. Wrapping a string around a circular object is one way to measure its circumference.
In this assignment, you will investigate the relationship of the circumference of a circle to its diameter.

Materials needed:

• string
• centimeter ruler or meter stick
• at least four circular objects of various sizes, such as circular discs or containers with circular bases

a. Use this table to record your measurements of  each circle's circumference and diameter:

Measure the circumference of a circular part of each object:

• wrap a string carefully around a circle and mark the length on the string with the end of your finger
• stretch the string along the ruler or meter stick and measure the circumference of the circle to the nearest tenth of a centimeter
• record the circumference in the table

Measure the diameter of each circle: 

• use a string and ruler to find the longest measurement across the circle to the nearest tenth of a centimeter
• record the diameter in the table

b. Divide the circumference of each circle by its diameter and record the answer in the table in part a. Approximately, what is the multiplier between the circumferences and the diameters?

c. If the diameter of a circle is 9 cm, predict its approximate circumference without measuring it. Explain your thinking.

11-3 The ratio of the circumference of a circle to its diameter has been measured with increasing accuracy since before 1650 b.c. We call the ratio of the circumference to diameter . In English,  is spelled pi and is pronounced pie. It is an irrational number, which means that there is no way to write its exact value as a fraction with integers. The value of  is slightly greater than 3. Find the button marked  on your calculator.

a. Write down the decimal equivalent for , accurate to the nearest hundredth.

b. The fraction    is often used to approximate .  What is the decimal equivalent of    accurate to the nearest hundredth?

c. Generalize the relationship between circumference and diameter of a circle.That is, describe how you can calculate the circumference of any circle if you know the diameter, and how you can find the length of the diameter if you know the circumference.

11-4 The length to travel the circumference of the earth, such as around the equator, is approximately 24,900 miles. 

a. Calculate the approximate diameter of the earth to the nearest mile. Show your calculation.

b. Signals that travel across the Internet are often carried through fiber-optic cables and travel at the speed of light, approximately 186,000 miles every second. At this rate, how long would it take an email to travel the circumference of the earth?

11-5 Estimate, without using a calculator, the circumference or diameter for each of the following circles. Explain your thinking for each.

a. The diameter is 1 cm. What is the circumference? 

b. The diameter is 7.2 meters. What is the circumference?

c. The circumference is 1 mile. What is the diameter? 

d. The circumference is 12 inches. What is the diameter? 

11-6 Find the circumference of each of the circles described below. Explian your thinking for each.

a. Radius of 3 inches

b. Diameter of 27 cm