Diameter

The diameter of a circle is a line segment that passes through the center of the circle and has its endpoints on the circle. It is the longest chord of the circle and it divides the circle into two equal halves.

Formula

The formula to find the diameter (d) of a circle when the radius (r) is given is:

d = 2 * r

Properties of Diameter

The diameter is twice the length of the radius.
The diameter is the longest chord of the circle.
It passes through the center of the circle.
The diameter divides the circle into two equal semicircles.

Examples

Example 1: If the radius of a circle is 5 cm, find the diameter.

Solution: Using the formula, d = 2 * r, we get d = 2 * 5 = 10 cm. So, the diameter of the circle is 10 cm.

Example 2: If the diameter of a circle is 12 inches, find the radius.

Solution: Since d = 2 * r, we can rearrange the formula to solve for r: r = d / 2. Substituting the given value, we get r = 12 / 2 = 6 inches. So, the radius of the circle is 6 inches.

Study Guide

Here are some key points to remember about the diameter of a circle:

The diameter is a line segment passing through the center of the circle.
It is twice the length of the radius.
The formula to find the diameter is d = 2 * r.
The diameter divides the circle into two equal halves called semicircles.

Practice using the formula to find the diameter when the radius is given, and vice versa. Also, solve problems involving the diameter in real-life situations to strengthen your understanding of this concept.

◂Math Worksheets and Study Guides Sixth Grade. Volume

The resources above cover the following skills:

Geometry (NCTM)

Use visualization, spatial reasoning, and geometric modeling to solve problems.

Use geometric models to represent and explain numerical and algebraic relationships.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Select and apply techniques and tools to accurately find length, area, volume, and angle measures to appropriate levels of precision.

Develop strategies to determine the surface area and volume of selected prisms, pyramids, and cylinders.

Connections to the Grade 6 Focal Points (NCTM)

Measurement and Geometry: Problems that involve areas and volumes, calling on students to find areas or volumes from lengths or to find lengths from volumes or areas and lengths, are especially appropriate. These problems extend the students' work in grade 5 on area and volume and provide a context for applying new work with equations.