To find the total cost of the fencing for the semicircular statuary garden, we need to follow these steps:
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Calculate the radius of the semicircle:
- The diameter of the semicircle is given as 30 feet.
- The radius \( r \) is half the diameter: \[ r = \frac{\text{diameter}}{2} = \frac{30 \text{ feet}}{2} = 15 \text{ feet} \]
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Calculate the circumference of the full circle:
- The formula for the circumference \( C \) of a full circle is: \[ C = 2\pi r \]
- Substituting the radius: \[ C = 2 \pi (15 \text{ feet}) = 30\pi \text{ feet} \]
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Calculate the circumference of the semicircle:
- Since the garden is semicircular, we take half of the full circumference: \[ \text{Circumference of the semicircle} = \frac{30\pi}{2} = 15\pi \text{ feet} \]
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Calculate the cost of the fencing:
- The cost of the fencing per linear foot is $9.25. Therefore, the total cost \( \text{Total Cost} \) is calculated as follows: \[ \text{Total Cost} = \text{Fencing cost per foot} \times \text{Length of fencing} \]
- Substituting our values: \[ \text{Total Cost} = (9.25 \text{ dollars/foot}) \times (15\pi \text{ feet}) \]
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Calculating \( 15\pi \):
- To get the numerical value: \[ \pi \approx 3.14 \ 15\pi \approx 15 \times 3.14 = 47.1 \text{ feet} \]
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Calculating the total cost:
- Now substituting back into the total cost equation: \[ \text{Total Cost} \approx 9.25 \times 47.1 = 435.075 \]
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Final answer:
- Therefore, rounding to the nearest cent, the fencing will cost approximately: \[ \text{Total Cost} \approx $435.08 \]
So, the total cost of the fencing around the semicircular statuary garden is approximately $435.08.
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