Unit 5
Glossary
Accelerated 6
The area of a circle is the number of square units it covers. If a circle has radius \(r\) units, its area is \(\pi r^2\) square units.
For example, a circle has radius of 3 inches. Its area is \(\pi 3^2\), or \(9\pi\), square inches. This is about 28.3 square inches.
A circle is made of all the points that are the same distance from a given point. That given point is the center of the circle.
Every point on this circle is 5 cm away from point \(A\).
The circumference of a circle is the distance around the circle. If a circle has radius \(r\) units, its circumference is \(2\pi r\) units.
For example, a circle has a radius of 3 inches. Its circumference is \(2 \boldcdot \pi \boldcdot 3\), or \(6\pi\) inches. This is about 18.85 inches.
In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity. This number is called the constant of proportionality.
In this example, the constant of proportionality is 3.
The coordinate plane is one way to represent pairs of numbers. The plane is made of a horizontal number line and a vertical number line that cross at 0.
Pairs of numbers can be used to describe the location of a point in the coordinate plane.
Point \(R\) is located at \((3,\text-2)\). This means \(R\) is 3 units to the right and 2 units down from \((0,0)\).
A diameter is a line segment that goes from one point on a circle to another and passes through the center. The length of this segment is also called the diameter. Every diameter of a circle is the same length.
The origin is the point \((0,0)\) in the coordinate plane. This is where the horizontal axis and the vertical axis cross. The origin is sometimes marked with the symbol \(\mathcal{O}\).
There is a proportional relationship between the diameter and circumference of any circle. The constant of proportionality is pi. The symbol for pi is \(\pi\).
This relationship can be represented with the equation \(C=\pi d\), where \(C\) represents the circumference and \(d\) represents the diameter. In the graph, pi can be seen as the value of \(C\) when the value of \(d\) is 1.
Some approximations for \(\pi\) are \(\frac{22}{7}\), 3.14, and 3.14159.
In a proportional relationship, the values for one quantity are each multiplied by the same number to get the values for the other quantity.
This table shows a proportional relationship between \(s\) and \(p\). Each value of \(p\) is 4 times a value of \(s\). This relationship can be written as \(p = 4s\).
| \(s\) | \(p\) |
|---|---|
| 2 | 8 |
| 3 | 12 |
| 5 | 20 |
| 10 | 40 |