Question

question * the circumference of a circle is 11π inches. what is the area, in square inches, of the circle? express your answer in terms of π.

Explanation:

Step1: Recall circumference formula

The formula for the circumference of a circle is $C = 2\pi r$. Given $C=11\pi$, we set up the equation $11\pi=2\pi r$.

Step2: Solve for radius $r$

Divide both sides of the equation $11\pi = 2\pi r$ by $2\pi$. We get $r=\frac{11}{2}$ inches.

Step3: Recall area formula

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

Step4: Calculate the area

Substitute $r = \frac{11}{2}$ into the area formula: $A=\pi(\frac{11}{2})^{2}=\frac{121\pi}{4}$ square - inches.

Answer:

$\frac{121\pi}{4}$