A circle is a closed curve in which all points on the curve are equidistant from a fixed point called 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. The ratio of the circumference of a circle to its diameter is a constant value denoted by the Greek letter π (pi), which is approximately 3.14159. The formula for the circumference of a circle is C = 2πr, where r is the radius, and the formula for the area of a circle is A = πr^{2}.

**Radius:**The distance from the center of a circle to any point on the circle.**Diameter:**The distance across a circle passing through the center, equal to 2 times the radius.**Circumference:**The distance around the edge of a circle, given by the formula C = 2πr or C = πd, where d is the diameter.**Area:**The measure of the space enclosed by a circle, given by the formula A = πr^{2}.

**Circumference:** C = 2πr or C = πd (where r is the radius and d is the diameter)

**Area:** A = πr^{2} (where r is the radius)

- Find the circumference of a circle with a radius of 5 cm.
- Find the area of a circle with a diameter of 12 inches.

**Solution:** C = 2π(5) = 10π cm, or approximately 31.42 cm.

**Solution:** r = d/2 = 12/2 = 6 inches, A = π(6^{2}) = 36π square inches, or approximately 113.10 square inches.

In summary, a circle is a closed curve with all points equidistant from the center. The radius is the distance from the center to any point on the circle, the diameter is the distance across the circle passing through the center, the circumference is the distance around the edge of the circle, and the area is the measure of the space enclosed by the circle. Key formulas for circles include C = 2πr and A = πr^{2} for the circumference and area, respectively.

Study GuideAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations Worksheet/Answer key

Algebraic Equations Worksheet/Answer keyAlgebraic Equations

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 6 Curriculum Focal Points (NCTM)

Algebra: Writing, interpreting, and using mathematical expressions and equations

Students write mathematical expressions and equations that correspond to given situations, they evaluate expressions, and they use expressions and formulas to solve problems. They understand that variables represent numbers whose exact values are not yet specified, and they use variables appropriately. Students understand that expressions in different forms can be equivalent, and they can rewrite an expression to represent a quantity in a different way (e.g., to make it more compact or to feature different information). Students know that the solutions of an equation are the values of the variables that make the equation true. They solve simple one-step equations by using number sense, properties of operations, and the idea of maintaining equality on both sides of an equation. They construct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table.