Question

Find the length of the​ radius, the​ circumference, and the area of the circle. Use 3.14 for pi.
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Part 1
         
23.5 cm

Answer 1

To find the radius, circumference, and area of the circle given the diameter, we start with the following information:

1. **Diameter**: \( d = 23.5 \, \text{cm} \)

From the diameter, we can find the radius:

### Part 1: Radius
The radius \( r \) is half of the diameter:
\[
r = \frac{d}{2} = \frac{23.5 \, \text{cm}}{2} = 11.75 \, \text{cm}
\]

### Part 2: Circumference
The circumference \( C \) of a circle can be calculated using the formula:
\[
C = \pi \cdot d
\]
Substituting \( d = 23.5 \, \text{cm} \) and \( \pi \approx 3.14 \):
\[
C = 3.14 \cdot 23.5 \approx 73.09 \, \text{cm}
\]

### Part 3: Area
The area \( A \) of a circle can be calculated using the formula:
\[
A = \pi \cdot r^2
\]
Substituting \( r = 11.75 \, \text{cm} \) and \( \pi \approx 3.14 \):
\[
A = 3.14 \cdot (11.75)^2
\]
Calculating \( (11.75)^2 \):
\[
(11.75)^2 = 138.0625
\]
So:
\[
A \approx 3.14 \cdot 138.0625 \approx 433.654375 \, \text{cm}^2
\]
Rounding to two decimal places:
\[
A \approx 433.65 \, \text{cm}^2
\]

### Summary of Results
- **Radius**: \( 11.75 \, \text{cm} \)
- **Circumference**: \( 73.09 \, \text{cm} \)
- **Area**: \( 433.65 \, \text{cm}^2 \)