Question

the circumference of a circle is 119.32 millimeters. what is the circles area?
c = 119.32 mm
round your answer to the nearest hundredth.
square millimeters

Explanation:

Step1: Recall the formula for the circumference of a circle

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius of the circle. We can solve for \( r \) by rearranging the formula: \( r=\frac{C}{2\pi} \). Given \( C = 119.32 \) mm and using \( \pi\approx3.14 \), we substitute the values: \( r=\frac{119.32}{2\times3.14} \).

Step2: Calculate the radius

First, calculate the denominator: \( 2\times3.14 = 6.28 \). Then, divide the circumference by the denominator: \( r=\frac{119.32}{6.28}=19 \) mm.

Step3: Recall the formula for the area of a circle

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). Now that we know \( r = 19 \) mm and \( \pi\approx3.14 \), we substitute these values into the formula: \( A = 3.14\times19^{2} \).

Step4: Calculate the area

First, calculate \( 19^{2}=361 \). Then, multiply by \( 3.14 \): \( A = 3.14\times361 = 1133.54 \) square millimeters.

Answer:

\( 1133.54 \)