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Video: Finding the Circumference of a Circle Given a Radius

Tim Burnham

Work out the circumference of the circle given that 𝑂𝐴 = 5, giving your answer accurate to two decimal places.

02:50

Video Transcript

Work out the circumference of the circle given that 𝑂𝐴 equals five, giving your answer accurate to two decimal places. So we’re told that length 𝑂𝐴 equals five, and we’re not actually told what the units are, so we don’t know whether they’re metres, miles, inches, whatever. So we’ll just have to write that on our diagram.

Now, 𝑂𝐴 marks out the distance here from the centre of the circle to its circumference, and we’ve got a special name for that; it’s the radius of the circle. So the radius of our circle is five units. Now the question asks us to work out the length of the circumference of the circle.

Now we’ve got two different formulae for working out the circumference: two times 𝜋 times 𝑟, where 𝑟 is the radius, or 𝜋 times 𝑑, where 𝑑 is the diameter. And since we’ve been given the radius in our question, then I think we’ll use this version of the formula.

So all I need to do is to plug the radius into that formula, so the circumference is two times 𝜋 times the radius of five, and two times five is ten. So our answer in terms of 𝜋 is ten 𝜋 units, but the question didn’t ask for that; it asked us to give our answer accurate to two decimal places.

Now we need to get our calculator out. 𝜋 is an irrational number, which means it’s got an infinite number of decimal places and they’re constantly changing, so we can’t hope to remember all of that number. We’re gonna have to use our calculator and get an approximation.

Now when I type ten times 𝜋 on my calculator, I get thirty-one point four one five nine two six five four, and then my calculator runs out of digits. But anyway, that’s enough accuracy to give our answer correct to decimal places. So what we need to do is, first of all, cover up everything after the second decimal place, which gives us thirty-one point four one, and then we just need to check the third decimal place to see whether we need to round the one up to a two or whether it can stay as a one.

And looking at the next digit, it’s a five. So the rule is if that next digit is zero, one, two, three, or four then the one stays as it is, a one, but if it’s a five, six, seven, eight, or nine then the one would need to be rounded up to a two.

And in our case, it’s a five, so we do need to round up the one to a two. So what that actually tells us is that the answer is closer to thirty-one point four two than it was to thirty-one point four one; that’s why we rounded the one up to a two, so the answer is thirty-one point four two units to two decimal places.