Question

the area of a circle is 81π cm². what is the circumference, in centimeters? express your answer in terms of π.

Explanation:

Step1: Find the radius

The area formula of a circle is $A = \pi r^{2}$. Given $A = 81\pi$, we have $\pi r^{2}=81\pi$. Divide both sides by $\pi$: $r^{2}=81$, so $r = 9$ cm (we take the positive value since radius is non - negative).

Step2: Calculate the circumference

The circumference formula of a circle is $C = 2\pi r$. Substitute $r = 9$ into the formula: $C=2\pi\times9 = 18\pi$ cm.

Answer:

$18\pi$