7.5.b 7.9.b 7.GSR.4 7.GSR.5

Circles 7th Grade

Texas Essential Knowledge and Skills (TEKS): 7.5.b
describe as the ratio of the circumference of a circle to its diameter; and
Texas Essential Knowledge and Skills (TEKS): 7.9.b
determine the circumference and area of circles;
Georgia Standards of Excellence (GSE): 7.GSR.4
Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of a circle.
Georgia Standards of Excellence (GSE): 7.GSR.5
Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.

Circumference and Area of a Circle

The diameter of a circle is the distance from one point on the circle to another point on the circle, through its center.

The radius of a circle is the distance from its center to a point on the circle.
The length of a circle's radius is half the length of its diameter.

The circumference of a circle is the distance around the circle.

Pi (

π

) is a non-repeating, non-terminating decimal which is equivalent to the ratio of a circle's circumference to its diameter. 3.14 is often used as an approximation of pi.

Circumference =

π

d or 2

π

r

Area =

π

r²

\begin{array}{rcl} Area & = & π r^{2} \\ 100 π {cm}^{2} & = & π r^{2} \\ 100 π {cm}^{2} \div π & = & π r^{2} \div π \\ 100 {cm}^{2} & = & r^{2} \\ \sqrt{100 {cm}^{2}} & = & \sqrt{r^{2}} \\ 10 cm & = & r \end{array}

\begin{array}{rcl} Circumference & = & 2 π r \\ = & 2 π (10 cm) \\ = & 20 π cm \end{array}

Circles

Texas Essential Knowledge and Skills (TEKS): 7.5.b

describe as the ratio of the circumference of a circle to its diameter; and

Texas Essential Knowledge and Skills (TEKS): 7.9.b

determine the circumference and area of circles;

Georgia Standards of Excellence (GSE): 7.GSR.4

Explore and describe the relationship between pi, radius, diameter, circumference, and area of a circle to derive the formulas for the circumference and area of a circle.

Georgia Standards of Excellence (GSE): 7.GSR.5

Given the formula for the area and circumference of a circle, solve problems that exist in everyday life.

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