☰ Contents · Geometry

Review and the circumference of a circle

Lessons 41–42 · 2 lessons · B. Xaydarov, E. Sariqov, A. Qo‘chqorov. Geometry, Grade 9 (textbook for general secondary schools), revised 4th edition. Huquq va Jamiyat Publishing, Tashkent, 2019
42

Circumference of a circle

Textbook: pp. 116–117
GoalKnow that the ratio of circumference to diameter is the constant π; apply C = 2πR.
New words
circumference C · aylana uzunligi Cthe number π · π soniC = 2πR · C = 2πRdiameter d · diametr d
Explanation

For every circle the ratio of its circumference C to its diameter d is the same number, which we denote by the letter π (pi): C/d = π. π is an irrational number, approximately 3.14. Since the diameter is twice the radius, the circumference is C = πd = 2πR. From this we also get R = C/(2π). The circumference is directly proportional to the radius: doubling the radius doubles the circumference. For example, a wheel that makes one full turn travels a distance equal to its circumference.

Worked examples
If R = 7 then C = 2π·7 = 14π.
If C = 20π then R = C/(2π) = 10 and d = 20.
Class activity

“Measure with string”: wrap a string around a glass or a lid, measure its length and then the diameter with a ruler, and compute C : d; the result is close to 3.14.

Practice
1
What is the circumference of a circle of radius 9 cm?
2
What is the circumference of a circle with diameter 5 m?
3
A circle has circumference 16π cm. What is its radius?
4
Why is C/d the same for all circles?