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

1 answer

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.