Question

the circumference of a circle is 76.616 millimeters. what is the circles area? 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. We know \( C = 76.616 \) millimeters, so we can solve for \( r \).

First, rearrange the formula to solve for \( r \): \( r=\frac{C}{2\pi} \)

Substitute \( C = 76.616 \) and \( \pi\approx3.14 \) (we'll use this approximation for calculation):

\( r=\frac{76.616}{2\times3.14}=\frac{76.616}{6.28} \)

Calculate the division: \( \frac{76.616}{6.28} = 12.2 \) millimeters. So the radius \( r = 12.2 \) mm.

Step2: Recall the formula for the area of a circle.

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). Now we substitute \( r = 12.2 \) and \( \pi\approx3.14 \) into the formula.

First, calculate \( r^{2} \): \( r^{2}=(12.2)^{2}=12.2\times12.2 = 148.84 \)

Then, calculate the area: \( A = 3.14\times148.84 \)

\( 3.14\times148.84=467.3576 \)

Step3: Round to the nearest hundredth.

The number \( 467.3576 \) rounded to the nearest hundredth (two decimal places) is \( 467.36 \) (since the third decimal place is 7, which is greater than or equal to 5, we round up the second decimal place: \( 5 + 1 = 6 \)).

Answer:

\( 467.36 \)