~ 3.8 ~

Learning Targets

• I can explain how the area of a circle and its circumference are related to each other.
• I know the formula for area of a circle.

Let’s rearrange circles to calculate their areas.

If C is a circle’s circumference and r is its radius, then C = 2 π r. The area of a circle can be found by taking the product of half the circumference and the radius.

If A is the area of the circle, this gives the equation:

A = ½ (2πr) ⋅ r

This equation can be rewritten as:

A = π r²

This means that if we know the radius, we can find the area. For example, if a circle has radius 10 cm, then the area is about (3.14) ⋅ 100 which is 314 cm².

If we know the diameter, we can figure out the radius, and then we can find the area. For example, if a circle has a diameter of 30 ft, then the radius is 15 ft, and the area is about (3.14) ⋅ 225 which is approximately 707 ft².

Today you are making a poster.

In the past, you decomposed and rearranged a shape to figure out its area! Each of you needs a circular object, a marker, and a color piece of paper.

1. Using a thick marker, trace your circle in 2 separate places on the colored paper.
2. Cut out both circles, cutting around the marker line.
3. Fold and cut one of the circles into fourths.
4. Arrange the fourths so that straight sides are next to each other, but the curved edges are alternately on top and on bottom.
5. Fold and cut the fourths in half to make eighths. Arrange the eighths next to each other, like you did with the fourths.
6. If your pieces are still large enough, repeat the previous step to make sixteenths.

*Watch the video below if you need help*