Unit 36 - Area of a Circle
Area of a Circle
Objectives At the end of the lesson, the students are expected to:- Approximate the area of a circle.
- Understand the formula for the area of a circle.
- compass
- ruler
- circular papers
- scissors
- Group students into pairs or groups of three.
- Provide each group with circular paper cutouts and scissors.
- Instruct them to cut the circle into equal slices.
- After cutting, have them approximate the area of the individual slices and the entire circle.
- Ask students to rearrange the slices to form a rectangle-like shape and approximate its area.
- Ask students why cutting the circle from the center produces 'better' slices.
- Discuss how many slices they would like to divide the circle into.
- Encourage different groups to use varying numbers of slices so students can observe that the more slices there are, the more the rearranged shape resembles a rectangle.
- Guide them in finding the length and width of the 'rectangle.' They should discover that one dimension corresponds to half of the circumference of the circle.
- Have students find the formula for the area of the rectangle and explain how it relates to the area of the original circle.
- Emphasize that as the number of slices increases, the rearranged shape becomes more like a rectangle. Eventually, it can be approximated as a rectangle.
- Show students the GeoGebra applet at https://www.geogebra.org/m/hef22tzd and move the slider to n = 100.
- Write the formula for finding the area of a circle: pi = r x r