Investigating the Area of a Circle
Create the formula to determine the area of a circle by dissecting the circle into segments and then reorganising them.
Question Time:
Respond to the following questions based on the graph above, either individually or collaboratively to establish deeper mathematical relations.
Basic: As the circle is rearranged and the number of parts increases, what shape do the reorganised parts begin to look like?
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- A
- B
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- D
Medium: The formula of the area of a parallelogram is A = b x h. If a circle is rearranged into many parts that look like a parallelogram, what is the measure of the height and what is the measure of the base? (based on the circle)
Advanced: What is the relationship between the formula for calculating the area of a circle and the formula for calculating the area of the parallelogram created by rearranging the sectors of the circle?