Question Video: Finding the Circumference of a Circle Given a Diameter

Work out the circumference of the circle, giving your answer accurate to two decimal places.

02:45

Video Transcript

Work out the circumference of the circle, giving your answer accurate to two decimal places.

In this example, we’re given the distance from one end of the circle to the other end of the circle through the center, and that’s called the diameter of a circle.

Our question is asking us to find the circumference. The circumference can be found in one of two ways: two times 𝜋 times 𝑟, which is the radius, or 𝜋 times 𝑑, which is the diameter.

In our case, we’ve already been given the diameter of the circle, so let’s use 𝜋 times 𝑑. To find the circumference, we’ll multiply 𝜋 times the diameter. Our diameter is six. We need to multiply six times 𝜋, and we want our answer to be accurate to two decimal places.

At this point, we can pull out our calculator to multiply six times 𝜋. My calculator gave me this: 18.84955592 and then it stops, but I know that this number goes on to infinity because 𝜋 is an irrational number.

We’re interested in rounding accurate to two decimal places. To accurately round here, we’ll need to look at what value is to the right of our two decimal places, to the right of the four. If the digit to the right of the four is between zero and four, we don’t round up. If the digit to the right of the four is between five and nine, we will round up.

Here the number to the right of the four is nine, which means we should round up. The four that was in the hundredths place becomes a five. This tells us that our answer is closer to 18.85 than it was to 18.84.

Now our answer is still missing one thing: how are we measuring the circumference? The circumference is 82 and 85 what? Units, we weren’t given a specific unit, so we just say that our diameter is six units. And then we say the circumference of this circle is 18.85 units.

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