To find the diameter, area, and circumference of a circle, we will use the following equations:
1. Diameter Equation
The diameter \(D\) of a circle is twice the radius \(r\): \[ D = 2r \]
2. Area Equation
The area \(A\) of a circle is given by the formula: \[ A = \pi r^2 \]
3. Circumference Equation
The circumference \(C\) of a circle is given by the formula: \[ C = 2\pi r \]
Now, let's calculate each of these using the provided radius of the middle circle, which is \(29\) ft.
Calculations
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Diameter: \[ D = 2r = 2 \times 29 = 58 \text{ ft} \]
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Area: \[ A = \pi r^2 = \pi \times (29)^2 = \pi \times 841 \approx 2641.59 \text{ ft}^2 \quad (\text{using } \pi \approx 3.14159) \]
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Circumference: \[ C = 2\pi r = 2\pi \times 29 \approx 182.21 \text{ ft} \quad (\text{using } \pi \approx 3.14159) \]
Summary of Results
- Diameter: \( 58 \text{ ft} \)
- Area: \( 2641.59 \text{ ft}^2 \)
- Circumference: \( 182.21 \text{ ft} \)
In conclusion, using your given radius of \(29\) ft, we calculated the diameter as \(58\) ft, the area as approximately \(2641.59\) ft², and the circumference as approximately \(182.21\) ft.