7.G.B.4 7th Grade Geometry

Circumference & Area of Circles

Know the formulas for the area and circumference of a circle, and use them to solve problems and explain the relationship between them.

How to explain it

At this standard, students apply the formulas for circumference (C=πd or C=2πr) and area (A=πr²) of a circle to solve real-world and mathematical problems, and identify common formula-application errors.

The anchor students hold onto: Circumference: C=πd or C=2πr (distance around). Area: A=πr² (space inside). Always use radius in the area formula. If given d, find r=d/2 first.

Circle formulas for circumference and area are foundational for 8.G.C.9, where students find surface area and volume of cylinders, cones, and spheres.

Worked examples

Example 1 Circumference

d=8 cm, find C

Step 1Choose formula: C=πd.

Step 2Substitute: C=π(8).

Step 3Calculate: C=3.14(8)=25.12 cm.

AnswerC=25.12 cm

Example 2 Area

r=5 cm, find A

Step 1Choose formula: A=πr².

Step 2Substitute: A=π(5²)=π(25).

Step 3Calculate: A=3.14(25)=78.5 cm².

AnswerA=78.5 cm²

Common mistakes

What students write Using diameter instead of radius in the area formula: writing A=πd² instead of A=πr².

The fix The area formula A=πr² requires the RADIUS. For d=10, find r=5 first: A=π(5²)=π(25)=78.5, not π(100)=314. Using d gives an area 4 times too large.

Try this A circle has a diameter of 12 cm. Rivera computes the area: "A=π×12²=π×144=452.16 cm²." Identify Rivera's error and find the correct area. Use π≈3.14.

What students write Using the circumference formula for area: writing A=πr instead of A=πr².

The fix The area formula has an EXPONENT: A=πr². Circumference is C=πd or C=2πr. Area has r SQUARED. Write both formulas on your reference card and check which you need.

Try this A circle has a radius of 5 cm. Tran computes the area: "A=π×r=π×5=15.7 cm²." Identify Tran's error and find the correct area. Use π≈3.14.

Teacher tip

Head off the two predictable errors before they happen. First: The area formula A=πr² requires the RADIUS. For d=10, find r=5 first: A=π(5²)=π(25)=78.5, not π(100)=314. Using d gives an area 4 times too large. Second: The area formula has an EXPONENT: A=πr². Circumference is C=πd or C=2πr. Area has r SQUARED. Write both formulas on your reference card and check which you need.