A circle is a closed curve where all points are equidistant from the center. The distance from the center to any point on the circle is called the radius, and the distance across the circle passing through the center is called the diameter.

**Radius:**The distance from the center of the circle to any point on the circle.**Diameter:**The distance across the circle passing through the center, and it is twice the length of the radius.**Circumference:**The perimeter of the circle, given by the formula C = 2πr or C = πd, where r is the radius and d is the diameter.**Area:**The space enclosed by the circle, given by the formula A = πr^{2}.

Here are the key formulas related to circles:

- Circumference: C = 2πr or C = πd
- Area: A = πr
^{2}

1. Find the circumference of a circle with radius 5 cm.

2. What is the area of a circle with diameter 12 m?

3. If the circumference of a circle is 31.4 cm, find its radius.

4. A circle has an area of 64π square units. Find its radius.

1. Circumference = 2πr = 2 * 3.14 * 5 = 31.4 cm

2. Radius = d/2 = 12/2 = 6 m, Area = πr^{2} = π * 6^{2} = 36π square meters

3. Circumference = 2πr, 31.4 = 2 * 3.14 * r, r = 31.4 / (2 * 3.14) = 5 cm

4. Area = πr^{2}, 64π = πr^{2}, r^{2} = 64, r = 8 units

Understanding the concepts of radius, diameter, circumference, and area of a circle is essential for solving problems related to circles. Practice using the formulas and solving problems to improve your skills in this topic.

Study GuideMeasurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference Worksheet/Answer key

Measurement, Perimeter, and Circumference

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 and use formulas to determine the circumference of circles and the area of triangles, parallelograms, trapezoids, and circles and develop strategies to find the area of more-complex shapes.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.