Question
Which chart shows the correct circumference and area of a circle with a radius of 27 m
Radius is 27 m, circumference 169.56 m, area 84.78 m²
Radius 27 m, circumference 2289.06 m, area 169.56 m²
Radius is 27 m, circumference 169.56 m, area, 2289.06 m²
Radius 27 m, circumference 84.78 m, area, 2289.06 m²
Radius is 27 m, circumference 169.56 m, area 84.78 m²
Radius 27 m, circumference 2289.06 m, area 169.56 m²
Radius is 27 m, circumference 169.56 m, area, 2289.06 m²
Radius 27 m, circumference 84.78 m, area, 2289.06 m²
Answers
GPT-4o mini
To calculate the circumference and area of a circle given the radius, you can use the following formulas:
1. **Circumference (C)**:
\[
C = 2 \pi r
\]
2. **Area (A)**:
\[
A = \pi r^2
\]
For a radius \( r = 27 \, m \):
1. **Circumference**:
\[
C = 2 \pi (27) \approx 2 \times 3.14159 \times 27 \approx 169.65 \, m
\]
2. **Area**:
\[
A = \pi (27)^2 \approx 3.14159 \times 729 \approx 2290.42 \, m^2
\]
Now, let's evaluate the given options based on our calculations:
- **First option**: Radius is 27 m, circumference 169.56 m, area 84.78 m² (Incorrect area)
- **Second option**: Radius 27 m, circumference 2289.06 m, area 169.56 m² (Incorrect circumference and area)
- **Third option**: Radius is 27 m, circumference 169.56 m, area 2289.06 m² (Correct circumference, incorrect area)
- **Fourth option**: Radius 27 m, circumference 84.78 m, area 2289.06 m² (Incorrect circumference)
The correct values for a radius of 27 m are:
- Circumference: approximately 169.65 m (close to 169.56 m)
- Area: approximately 2290.42 m² (close to 2289.06 m²)
Therefore, the **third option** is the only one that closely matches the correct circumference and the area (although the area is slightly inaccurate).
1. **Circumference (C)**:
\[
C = 2 \pi r
\]
2. **Area (A)**:
\[
A = \pi r^2
\]
For a radius \( r = 27 \, m \):
1. **Circumference**:
\[
C = 2 \pi (27) \approx 2 \times 3.14159 \times 27 \approx 169.65 \, m
\]
2. **Area**:
\[
A = \pi (27)^2 \approx 3.14159 \times 729 \approx 2290.42 \, m^2
\]
Now, let's evaluate the given options based on our calculations:
- **First option**: Radius is 27 m, circumference 169.56 m, area 84.78 m² (Incorrect area)
- **Second option**: Radius 27 m, circumference 2289.06 m, area 169.56 m² (Incorrect circumference and area)
- **Third option**: Radius is 27 m, circumference 169.56 m, area 2289.06 m² (Correct circumference, incorrect area)
- **Fourth option**: Radius 27 m, circumference 84.78 m, area 2289.06 m² (Incorrect circumference)
The correct values for a radius of 27 m are:
- Circumference: approximately 169.65 m (close to 169.56 m)
- Area: approximately 2290.42 m² (close to 2289.06 m²)
Therefore, the **third option** is the only one that closely matches the correct circumference and the area (although the area is slightly inaccurate).