Lesson · Grade 7 · Mathematics
Diameter from circumference
- Grade 7
- Mathematics
- 1 min 18 s
- British Columbia
- BC7-MA-49
A circle 31.4 cm around is rolled out flat, and just over 3 diameters (3.14, which is pi) fit along it, so the circumference is pi times the diameter and the diameter is the circumference divided by pi. The worked example finds d ≈ 31.4 ÷ 3.14 ≈ 10 cm, checks it with 3.14 × 10 = 31.4, and ends on the one-line recap d = C ÷ π.
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In one sentence
The question this lesson answers
A piece of string that goes once around this circle is 31.4 centimetres long.
How long is its diameter, the distance straight across through the centre?
Transcript
What the lesson says
A piece of string that goes once around this circle is 31.4 centimetres long.
How long is its diameter, the distance straight across through the centre?
Let us roll the circle along, so its circumference lies flat in a straight line.
Now lay copies of the diameter along that line, one after another.
Three whole diameters fit, plus a small piece about 0.14 of a diameter long.
About 3.14 diameters fit around every circle, and that number is called pi.
So the circumference is pi times the diameter.
Dividing undoes multiplying, so the diameter is the circumference divided by pi.
Our circumference is 31.4 centimetres, so divide 31.4 by 3.14.
The diameter is about 10 centimetres.
To check, 3.14 times 10 is 31.4, which is the circumference we started with.
Remember, to find the diameter, divide the circumference by pi.
Curriculum
Where this fits
- British Columbia, Grade 7
Mathematics, Geometry and measurement: circumference and area of circlesBC7-MA-49
Previous: Circumference from Diameter or RadiusNext: Why the Area of a Circle Is π × r × r
The outcomes and strands follow the British Columbia curriculum.
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