Embedded Files
Learning Targets
I can write exact answers in terms of π.
I can calculate the area of more complicated shapes that include fractions of circles.
Notes
Notes
The relationship between A, the area of a circle, and r, its radius, is A=πr2. We can use this to find the area of a circle if we know the radius. For example, if a circle has a radius of 10 cm, then the area is π⋅102 or 100π cm2. We can also use the formula to find the radius of a circle if we know the area. For example, if a circle has an area of 49π m2 then its radius is 7 m and its diameter is 14 m.
Sometimes instead of leaving π in expressions for the area, a numerical approximation can be helpful. For the examples above, a circle of radius 10 cm has area about 314 cm2. In a similar way, a circle with area 154 m2 has radius about 7 m.
We can also figure out the area of a fraction of a circle. For example, the figure shows a circle divided into 3 pieces of equal area. The shaded part has an area of ⅓ π r2.
Activities
Activities
9.2 Comparing Areas Made of Circles
9.2 Comparing Areas Made of Circles
*Hint* Deconstruct the shapes.
1. Each square has a side length of 12 units. Compare the areas of the shaded regions in the 3 figures. Which figure has the largest shaded region? Explain or show your reasoning.
2. Each square in Figures D and E has a side length of 1 unit. Compare the area of the two figures. Which figure has more area? How much more? Explain or show your reasoning.
9.3 The Running Track Revisited
9.3 The Running Track Revisited
The field inside a running track is made up of a rectangle 84.39 m long and 73 m wide, together with a half-circle at each end. The running lanes are 9.76 m wide all the way around.
What is the area of the running track that goes around the field? Explain or show your reasoning.
Assignment
Assignment
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