Video: Finding the Circumference of a Circle given Its Area

Find the circumference of a circle whose area is 9.625 cmΒ². Use πœ‹ = 22/7.

02:41

Video Transcript

Find the circumference of a circle whose area is 9.625 centimetres squared. Use πœ‹ equals 22 over seven.

So in this question, we have two key bits of information. First of all, we have that the area is equal to 9.625. And we’re told to use a value of πœ‹, that is, 22 over seven. Now, we need to have a look at what the question is looking for. Well, the question wants us to find the circumference. So how we’re going to do that. Well, the circumference of a circle is equal to πœ‹π‘‘. Another way of writing it is two πœ‹π‘Ÿ. And that’s because if we look at the sketch I’ve drawn here, the diameter is twice the radius. So the diameter is equal to two π‘Ÿ or two multiplied by π‘Ÿ.

Okay, so what are we missing from the information we’ve got to be able to find the circumference? Well, we don’t have the diameter or the radius. So that’s what we need to find first if we want to find the circumference. Well, what we can use to help us find the radius is another equation. And that is that the area is equal to πœ‹π‘Ÿ squared. And we can use that because we know what the area is because we’re told what it is in the question.

So if we have 𝐴 is equal to πœ‹π‘Ÿ squared, we can now substitute in our value for the area and our value for πœ‹. So then, what we need to do is divide each side of the equation by 22 over seven. And when we do that, we get 3.0625 is equal to π‘Ÿ squared.

And now we’re looking for π‘Ÿ. So we’ve got π‘Ÿ squared. So what we need to do is the inverse square. So we’re gonna take the square root of both sides. And when we do that, we get a value for π‘Ÿ. And that π‘Ÿ value is 1.75, which also means we can work out a value for 𝑑 or diameter cause this will be two multiplied by 1.75, which will be 3.5. So great, we have all the bits of information we need now to help us find our circumference.

Because we have both the radius and the diameter, we could use either πœ‹π‘‘ or two πœ‹π‘Ÿ. I’m gonna use πœ‹π‘‘. So what we need to do now is substitute in our value for 𝑑 and our value for πœ‹ into 𝐢 equals πœ‹π‘‘. And when we do that, we’re gonna get 𝐢, the circumference, is equal to 22 over seven multiplied by 3.5.

So therefore, we can say that the circumference of a circle whose area is 9.625 centimetres squared, when we use πœ‹ to be 22 over seven, is 11 centimetres.

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