Problem 7.4 Remember: A radius square is a square whose sides are the same length as the radius of the circle.
Part A For each circle, cut out several copies of the radius square from a transparency sheet of centimeter grid paper. Find out how many radius squares it takes to cover the circle. You may cut the radius squares into parts if you need to Record your data in a table with these column headings: Circle Radius of Area of Area of Number of Circle Radius Square Circle Radius Squares Needed
Part B Now draw a couple of your own circles on grid paper. Make radius squares for each circle, and find out how many radius squares it takes to cover each circle. Add this data to your table.
Part C We are now going to test our theory on area of circles with a different unit of measurement. Use labsheet 7.4. Cover your radius square with Skittles and count them. Cover your circle with Skittles and count them. Divide the number of Skittles covering the circle by the number that covered the radius square. What do you discover from your explorations? Chart this on the table.
Part D Describe any patterns you see in your data.
Part E If you were asked to estimate the area of any circle in radius squares, what would you report as the best estimate?
Follow-up How can you find the area of a circle if you know the diameter or the radius? How can you find the diameter or radius of a circle if you know the area?