Question

which statement describes how to use the circumference of a circle to find its area?
a divide the circumference by 2
b multiply the circumference by the radius
c divide the circumference by π and then divide by 2
d divide the circumference by 2 and then multiply by the radius

Explanation:

Step1: Recall the formula for circumference

The formula for the circumference of a circle is \(C = 2\pi r\).

Step2: Solve for radius

From \(C = 2\pi r\), we can solve for \(r\) (radius) by \(r=\frac{C}{2\pi}\).

Step3: Recall the formula for area

The formula for the area of a circle is \(A=\pi r^{2}\).

Step4: Substitute \(r\) into area formula

Substitute \(r = \frac{C}{2\pi}\) into \(A=\pi r^{2}\), we get \(A=\pi(\frac{C}{2\pi})^{2}=\frac{C^{2}}{4\pi}\).
Another way:
From \(C = 2\pi r\), first find \(r\) as \(r=\frac{C}{2\pi}\) (which is equivalent to divide the circumference \(C\) by \(\pi\) and then divide by 2).

Answer:

C. divide the circumference by \(\pi\) and then divide by 2