Answer:
B. [tex]2.25\pi \text{ inches}^2[/tex]
Step-by-step explanation:
We have been given that the circumference of a circle is [tex]3\pi[/tex] inches. We are asked to find the area of the circle.
Since we know that the circumference of a circle is [tex]2\pi r[/tex].
[tex]\text{Circumference}=2\pi r[/tex]
Upon substituting the circumference as [tex]3\pi\text{ inches}[/tex] we will get,
[tex]3\pi=2\pi r[/tex]
Let us divide both sides of our equation by [tex]2\pi[/tex].
[tex]\frac{3\pi\text{ inches}}{2\pi}=\frac{2\pi r}{2\pi}[/tex]
[tex]\frac{3}{2}\text{ inches}=r[/tex]
[tex]1.5\text{ inches}=r[/tex]
[tex]\text{Area of circle}=\pi r^2[/tex]
Upon substituting r=1.5 in area of circle formula we will get,
[tex]\text{Area of circle}=\pi*(1.5\text{ inches})^2[/tex]
[tex]\text{Area of circle}=\pi*2.25\text{ inches}^2[/tex]
Therefore, the area of circle will be [tex]2.25\pi \text{ inches}^2[/tex] and option B is the correct choice.
