Question

The circumference of a circle is 3pi in. What is the area of the circle?

Answer 1

The area of a circle with a circumference of 3π inches is 2.25π square inches, which is found by first determining the radius as 1.5 inches and then applying the area formula A = πr².

Step-by-step explanation:

To find the area of a circle where the circumference is given as 3π inches, we can first find the radius of the circle using the formula for the circumference, which is C = 2πr. From the given circumference, 3π, we can solve for r, the radius:

C = 2πr

3π = 2πr

3 = 2r

r = 1.5 inches

Once we have the radius, we can use the formula for the area of a circle, A = πr², to determine the area:

Area (A) = π(1.5²)

A = π(2.25)

A = 2.25π square inches

This is the area of the circle using the given circumference.

Answer 2

A = 2.25 pi in^2

Step-by-step explanation:

The circumference of a circle is 3pi

so d = 3

Area of circle = pi r^2

r = 3/2 = 1.5

A = (1.5)^2 pi

A = 2.25 pi in^2