To find the radius, circumference, and area of the circle given the diameter, we start with the following information:
- 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: \( 433.65 , \text{cm}^2 \)