Question

A museum groundskeeper is creating a semicircular statuary garden with a diameter of

30 feet. There will be a fence around the garden. The fencing costs $9.25per linear foot.

How much will the fencing cost altogether? Show all work to earn full credit.

Answer 1

To find the total cost of the fencing for the semicircular statuary garden, we need to follow these steps:

1. **Calculate the radius of the semicircle**:
- The diameter of the semicircle is given as 30 feet.
- The radius \( r \) is half the diameter:
\[
r = \frac{\text{diameter}}{2} = \frac{30 \text{ feet}}{2} = 15 \text{ feet}
\]

2. **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:
\[
C = 2 \pi (15 \text{ feet}) = 30\pi \text{ feet}
\]

3. **Calculate the circumference of the semicircle**:
- Since the garden is semicircular, we take half of the full circumference:
\[
\text{Circumference of the semicircle} = \frac{30\pi}{2} = 15\pi \text{ feet}
\]

4. **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:
\[
\text{Total Cost} = (9.25 \text{ dollars/foot}) \times (15\pi \text{ feet})
\]

5. **Calculating \( 15\pi \)**:
- To get the numerical value:
\[
\pi \approx 3.14 \\
15\pi \approx 15 \times 3.14 = 47.1 \text{ feet}
\]

6. **Calculating the total cost**:
- Now substituting back into the total cost equation:
\[
\text{Total Cost} \approx 9.25 \times 47.1 = 435.075
\]

7. **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**.