Question

Which chart shows the correct circumference and area of a circle with a radius of 27 m?(1 point)
Responses

Radius Circumference Area
27 m 169.56 m 84.78 m2
Radius Circumference Area 27 m 169.56 m 84.78 m squared

Radius Circumference Area
27 m 169.56 m 2,289.06 m2
Radius Circumference Area 27 m 169.56 m 2,289.06 m squared

Radius Circumference Area
27 m 84.78 m 2,289.06 m2
Radius Circumference Area 27 m 84.78 m 2,289.06 m squared

Radius Circumference Area
27 m 2,289.06 m 169.56 m2

Answer 1

To find the correct circumference and area of a circle with a radius of \(27\) m, we can use the following formulas:

1. **Circumference (C)** of a circle:
\[
C = 2 \pi r
\]
where \(r\) is the radius.

2. **Area (A)** of a circle:
\[
A = \pi r^2
\]

Now, substituting the value of the radius \(r = 27\) m:

1. **Circumference**:
\[
C = 2 \pi (27) \approx 2 \times 3.14159 \times 27 \approx 169.56 \, \text{m}
\]

2. **Area**:
\[
A = \pi (27)^2 \approx 3.14159 \times 729 \approx 2290.21 \, \text{m}^2
\]

Now we can analyze the options given:

1. **First Option**: Radius \(27 \, m\), Circumference \(169.56 \, m\), Area \(84.78 \, m^2\) -- incorrect area.
2. **Second Option**: Radius \(27 \, m\), Circumference \(169.56 \, m\), Area \(2,289.06 \, m^2\) -- close area value (rounding is possible).
3. **Third Option**: Radius \(27 \, m\), Circumference \(84.78 \, m\), Area \(2,289.06 \, m^2\) -- incorrect circumference.
4. **Fourth Option**: Radius \(27 \, m\), Circumference \(2,289.06 \, m\), Area \(169.56 \, m^2\) -- incorrect values.

The second option is the one that shows the correct circumference and a correct approximation of the area:

\[
\text{Radius: } 27 \, m, \, \text{Circumference: } 169.56 \, m, \, \text{Area: } 2,289.06 \, m^2
\]

Thus, the **correct choice** is the **second option**.