Video: Rearranging a Circumference Formula to Make Pi the Subject

The formula for the circumference of a circle is 𝐶 = 2𝜋𝑟. Rearrange this formula to make 𝜋 the subject.

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Video Transcript

The formula for the circumference of a circle is 𝐶 is equal to two 𝜋𝑟. Rearrange this formula to make 𝜋 the subject.

We are given in the question the formula for the circumference of a circle: 𝐶 is equal to two 𝜋𝑟. You might also have seen this as 𝜋𝑑, where 𝑑 is the diameter and twice the radius. We are asked to rearrange the formula to make 𝜋 the subject. In order to do this, we will use the balancing method and our knowledge of inverse operations.

In the formula 𝐶 equals two 𝜋𝑟, the two, 𝜋, and 𝑟 are all being multiplied together. The opposite or inverse of multiplying is dividing. We can therefore divide both sides of the formula by two 𝑟. On the right-hand side, both the twos and 𝑟’s will cancel. This gives us 𝐶 over two 𝑟 is equal to 𝜋.

We know that 𝜋 is equal to 3.1415 and so on. Rearranging this formula as we have done tells us that when we divide the length of the circumference of any circle by twice its radius, we always get 𝜋. We always get an answer of 3.1415 and so on. As the diameter is equal to twice the radius, 𝜋 is also equal to the circumference divided by the diameter.

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