Question

5a. A circle has a circumference of 131.95 meters. What is the diameter and how did you calculate it?

C = πd


You must show ALL work for full credit.

(2 points)
5b. What is the area for the same circle? How did you calculate it?

A = πr2


You must show ALL work for full credit.

(2 points)

Answer 1

To solve both parts of the problem, we will use the relationships between circumference, diameter, radius, and area of a circle.

### 5a. Calculate the Diameter

The formula for the circumference \( C \) of a circle is given by:

\[
C = \pi d
\]

Where:
- \( C \) is the circumference,
- \( d \) is the diameter,
- \( \pi \) (pi) is approximately \( 3.14159 \).

We know the circumference \( C \) is 131.95 meters, so we can rearrange the formula to solve for the diameter \( d \):

\[
d = \frac{C}{\pi}
\]

Plugging in the value of \( C \):

\[
d = \frac{131.95}{\pi} \approx \frac{131.95}{3.14159} \approx 42.00 \text{ meters}
\]

Thus, the diameter of the circle is approximately **42.00 meters**.

### 5b. Calculate the Area

To calculate the area \( A \) of the same circle, we use the formula:

\[
A = \pi r^2
\]

Where:
- \( A \) is the area,
- \( r \) is the radius of the circle.

Since the radius \( r \) is half of the diameter \( d \):

\[
r = \frac{d}{2} = \frac{42.00}{2} = 21.00 \text{ meters}
\]

Now we can plug the radius into the area formula:

\[
A = \pi r^2 = \pi (21.00)^2
\]

Calculating \( (21.00)^2 \):

\[
(21.00)^2 = 441.00
\]

Now substituting back into the area formula:

\[
A = \pi \times 441.00 \approx 3.14159 \times 441.00 \approx 1385.44 \text{ square meters}
\]

Thus, the area of the circle is approximately **1385.44 square meters**.

### Summary:

- **Diameter**: 42.00 meters
- **Area**: 1385.44 square meters