If the area of a circle measures 9/4 Ο€ cm 2, what is the circumference of the circle in terms of Ο€?

Accepted Solution

Given that the area of the circle = [tex] \frac{9}{4} \pi \; cm^2 [/tex].Now question says to find the circumference of the circle.Before finding circumference, we need to find the radius of the circle so let's use formula of area of circle which is :[tex] Area = \pi r^2 [/tex]plug the given value of area[tex] \frac{9}{4} \pi= \pi r^2 [/tex][tex] \frac{9}{4} = r^2 [/tex]take square root of both sides[tex] \frac{3}{2} = r [/tex]Now we can use formula of circuference to find the circumference of given circleCircumference [tex] = 2 \pi r [/tex]Circumference [tex] = 2 \pi *\frac{3}{2} [/tex]Circumference [tex] = \pi *3 [/tex]Circumference [tex] = 3 \pi [/tex]Hence final answer is [tex] =3 \pi [/tex] cm.