ASVAB Preparation: Circles
You will need to be familiar with some circle basics for the ASVAB. A circle is formed when the points of a closed line are all located an equal distance from its center. A circle always has 360 ͦ. Here are some key circle terms:
- Circumference (C): The closed line of a circle — that is, the distance around the circle — is called its circumference.
- Radius (r): The radius of a circle is the measurement from the center of the circle to any point on the circumference of the circle.
- Diameter (d): The diameter of the circle is measured as a line passing through the center of the circle, from a point on one side of the circle all the way to a point on the other side of the circle.
The diameter of a circle is always twice as long as the radius of a circle: a=2r.
Navigating the circumference
To measure the circumference of a circle, use the number pi (π). Although π is a lengthy number, it’s generally rounded to 3.14 or 22/7. If you round π so you can solve a problem, the equal sign isn’t used because the answer isn’t equal to the actual length. The approximation symbol (≈) is used.
The formula for circumference is circumference = π × diameter, or C = πd. Because the radius of a circle is half its diameter, you can also use the radius to determine the circumference of a circle. Here’s the formula: C = 2πr.
Suppose you know that the pie you just baked has a diameter of 9 inches. You can determine its circumference by using the circumference formula:
C = πd
C ≈ 3.14 × 9
C ≈ 28.26 inches
Mapping out the area
Determining the area of a circle also requires the use of π. Area = πx the square of the circle’s radius, or A = πr2.
To determine the area of a 9-inch-diameter pie, multiply π by the square of 4.5. Why 4.5 and not 9? Remember, the radius is always half the diameter, and the diameter is 9 inches.
A = xr2
A = 3.14 × 4.52
A = 3.14 × (4.5 × 4.5)
A = 3.14 × 20.25
A = 63.585 inches