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C d. = π. d .  d. P.O.D. #1. basic. advanced. W = 2 + 4r 2 If r = 3, what is the value of W?. B = 28 – 3.97t 3 If t = 2, what is the value of B?. W = 2 + 4  3 2 W = 2 + 4  9 W = 2 + 36 W = 38. B = 28 – 3.97  2 3 B = 28 – 3.97  8 B = 28 – 31.76 B = -3.76.

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C

d

= π

d 

 d


P.O.D. #1

basic

advanced

W = 2 + 4r2

If r = 3, what is the value of W?

B = 28 – 3.97t3

If t = 2, what is the value of B?

W = 2 + 4  32

W = 2 + 4  9

W = 2 + 36

W = 38

B = 28 – 3.97  23

B = 28 – 3.97  8

B = 28 – 31.76

B = -3.76



A circle is the set of all points in a plane that are the same distance from a point. We call this point the center of the circle.

C

Circumference (C): the distance around a circle

Diameter (d): the distance across a circle through its center

Radius (r): the distance from the center to any point on the circle

d

r


Pi (π) is the ratio of the circumference of a circle to its diameter.

Approximations of Pi

3.14

22

7


Pi with Pies diameter.


Ready, set, measure... diameter.

  • Student #1: Measure the circumference

  • Student #2: Measure the diameter

  • Student #3: Record the measurements

  • Student #4: Calculate the ratio of the circumference to the diameter


2 Ways to Calculate Circumference diameter.

C = πd

14

C = 2πr

7

C = π  14

C ≈ 22 14

7

C ≈ 22 2

C ≈ 44

C = 2π  7

C ≈ 2 22 7

7

C ≈ 222

C ≈ 44


Whiteboard: diameter.

Big Ben is a famous clock tower in London. The diameter of the clock face is 23 feet. Find the circumference of the clock face. Use 3.14 for π. Round to the nearest tenth.

C = πd

C ≈ 3.14  23ft

C ≈ 72.22 ft

C ≈ 72.2 ft


Whiteboard: diameter.

The Belknap shield volcano is located in the Cascade Range in Oregon. The volcano is circular and has a diameter of 5 miles. What is the circumference of this volcano?

C = πd

C ≈ 3.14  5 ft

C ≈ 15.7 ft


Group Ponder: diameter.

The largest tree in the world by volume is in Sequoia National Park. The diameter at the base is 36 feet. If each student reaches their arms out wide, how many students would it take to reach around the base of the tree?

  • What is the circumference of the tree?

  • How wide can the average student stretch out their arms?


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