### Video Transcript

Find the circumference of a circle whose area is 9.625 centimetres squared. Use π 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 weβre told to use a value of π, 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 weβre going to do that. Well, the circumference of a circle is equal to ππ. Another way of writing it is two ππ. And thatβs because if we look at the sketch Iβve drawn here, the diameter is twice the radius. So the diameter is equal to two π or two multiplied by π.

Okay, so what are we missing from the information weβve got to be able to find the circumference? Well, we donβt have the diameter or the radius. So thatβs 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 ππ squared. And we can use that because we know what the area is because weβre told what it is in the question.

So if we have π΄ is equal to ππ squared, we can now substitute in our value for the area and our value for π. 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 squared.

And now weβre looking for π. So weβve got π squared. So what we need to do is the inverse square. So weβre gonna take the square root of both sides. And when we do that, we get a value for π. And that π value is 1.75, which also means we can work out a value for π 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 ππ or two ππ. Iβm gonna use ππ. So what we need to do now is substitute in our value for π and our value for π into πΆ equals ππ. And when we do that, weβre gonna get πΆ, 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 to be 22 over seven, is 11 centimetres.