Question Video: Finding a Formula Linking the Area and Circumference of a Circle | Nagwa Question Video: Finding a Formula Linking the Area and Circumference of a Circle | Nagwa

# Question Video: Finding a Formula Linking the Area and Circumference of a Circle

Using the formulae for the circumference and area of a circle, eliminate the variable π to find a formula that allows you to calculate the area of a circle from its circumference.

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### Video Transcript

Using the formulae for the circumference and area of a circle, eliminate the variable π to find a formula that allows you to calculate the area of a circle from its circumference.

Letβs begin by recalling our formulae for this circumference and area of a circle. The circumference, π, is equal to π multiplied by the diameter, π. As the diameter is double the length of the radius, this can also be written as π is equal to two ππ. We will call this equation one. The area of a circle is equal to ππ squared. We will call π΄ equals ππ squared equation two.

We are asked to eliminate the variable π to find a formula that allows us to calculate the area from the circumference. One way to do this is to rearrange equation one to make π the subject. Dividing both sides of equation one by two π gives us π over two π is equal to π. We can then substitute this into equation two. We will replace π with π over two π. This gives us π΄ is equal to π multiplied by π over two π squared.

We recall that when squaring a fraction, we can square the numerator and denominator separately. In this case, we need to square π and two π. π multiplied by π is π squared and two π multiplied by two π is four π squared. We now have π΄ is equal to π multiplied by π squared divided by four π squared. We can divide the numerator and denominator by π.

π΄ is, therefore, equal to π squared over four π. This formula allows us to calculate the area of a circle, π΄, when given its circumference, π. We can also rearrange this formula to make the circumference, π, the subject. This would allow us to calculate the circumference of a circle from its area.

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