~ 3.9 ~
Applying Area of Circles
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
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
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
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
Check Google Classroom!