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Illustrative Math
Grade 7
Let’s use π to solve problems.
Illustrative Math Unit 7.3, Lesson 4 (printable worksheets)
The circumference of a circle, C, is π times the diameter, d. The diameter is twice the radius, r. So if we know any one of these measurements for a particular circle, we can find the others. We can write the relationships between these different measures using equations:
d = 2r
C = πd
C = 2πr
If the diameter of a car tire is 60 cm, that means the radius is 30 cm and the circumference is 60 · π or about 188 cm.
If the radius of a clock is 5 in, that means the diameter is 10 in, and the circumference is 10 · π or about 31 in.
If a ring has a circumference of 44 mm, that means the diameter is 44 ÷ π, which is about 14 mm, and the radius is about 7 mm.
Here are some pictures of circular objects, with measurement tools shown. The measurement tool on each picture reads as follows:
Wagon wheel: 3 feet
Plane propeller: 24 inches
Sliced Orange: 20 centimeters
In the previous activity, we looked at pictures of circular objects. One measurement for each object is listed in the table. Your teacher will assign an approximation for π for you to use in this activity.
The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at each end.
This size running track is usually called a 400-meter track. However, if a person ran as close to the “inside” as possible on the track, they would run less than 400 meters in one lap. How far away from the inside border would someone have to run to make one lap equal exactly 400 meters?
The distance of the two straight tracks are 84.39 m + 84.39 m = 168.78 m
To run 400 m, the circumference of the circle (formed by the two half-circles) would need to be 400 m - 168.78 m = 231.22 m
The diameter of the circle would be 231.22 ÷ π = 73.6 m
The diameter of the green area is 73 m.
So the person would need to run (73.6 - 73) ÷ 2 = 0.3 m from the inside border.
Kiran bent some wire around a rectangle to make a picture frame. The rectangle is 8 inches by 10 inches.
The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.
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