Diameter Study Guide

Definition:

The diameter of a circle is a straight line that passes through the center of the circle and touches two points on the circle.

Formula:

The formula to calculate the diameter of a circle is: d = 2r where d is the diameter and r is the radius of the circle.

Key Points:

1. The diameter is always twice the length of the radius.
2. The diameter is the longest chord of the circle.
3. The diameter is the distance across the circle through its center.

Examples:

Let's calculate the diameter of a circle with a given radius:

1. If the radius (r) is 5 units, then the diameter (d) = 2 x 5 = 10 units
2. If the radius (r) is 8.5 cm, then the diameter (d) = 2 x 8.5 = 17 cm

Practice Problems:

1. A circle has a radius of 6 inches. Calculate the diameter of the circle.

2. Find the diameter of a circle with a radius of 12 cm.

3. If the diameter of a circle is 20 meters, what is its radius?

Explanation of Practice Problems:

1. To find the diameter, use the formula d = 2r where r = 6 inches. Substituting the value of r, we get d = 2 x 6 = 12 inches.

2. Similarly, for a circle with r = 12 cm, the diameter is d = 2 x 12 = 24 cm.

3. To find the radius, use the formula r = d/2 where d = 20 meters. Substituting the value of d, we get r = 20 / 2 = 10 meters.