Question

the circumference of a circle is 7π m. what is the area, in square meters? express your answer in terms of π.

Explanation:

Step1: Recall the circumference formula

The formula for the circumference of a circle is $C = 2\pi r$, where $C$ is the circumference and $r$ is the radius. Given $C=7\pi$, we have $2\pi r=7\pi$.

Step2: Solve for the radius

Divide both sides of the equation $2\pi r = 7\pi$ by $2\pi$. So, $r=\frac{7\pi}{2\pi}=\frac{7}{2}$ m.

Step3: Recall the area formula

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

Step4: Calculate the area

Substitute $r = \frac{7}{2}$ into the area formula: $A=\pi(\frac{7}{2})^{2}=\pi\times\frac{49}{4}=\frac{49\pi}{4}$ $m^{2}$.

Answer:

$\frac{49\pi}{4}$