Question

The circumference of a circle is 3π in. What is the area of the circle? ​ 1.5π ​ in² ​ 2.25π ​ in² ​ 6π ​ in² ​ 9π ​ in²

Answer 1

Answer:

B. $2.25\pi \text{ inches}^2$

Step-by-step explanation:

We have been given that the circumference of a circle is $3\pi$ inches. We are asked to find the area of the circle.

Since we know that the circumference of a circle is $2\pi r$.

$\text{Circumference}=2\pi r$

Upon substituting the circumference as $3\pi\text{ inches}$ we will get,

$3\pi=2\pi r$

Let us divide both sides of our equation by $2\pi$.

$\frac{3\pi\text{ inches}}{2\pi}=\frac{2\pi r}{2\pi}$

$\frac{3}{2}\text{ inches}=r$

$1.5\text{ inches}=r$

$\text{Area of circle}=\pi r^2$

Upon substituting r=1.5 in area of circle formula we will get,

$\text{Area of circle}=\pi*(1.5\text{ inches})^2$

$\text{Area of circle}=\pi*2.25\text{ inches}^2$

Therefore, the area of circle will be $2.25\pi \text{ inches}^2$ and option B is the correct choice.

Answer 2

C = 2πr
so
r = C/2π
r = 3π/2π
r = 3/2
r = 1.5

A = πr^2
A = π(1.5)^2
A = 2.25π 

answer
2.25π ​ in²