Question
Find the cost of sod, at $1.74 per square foot, for the playing field pictured. Use 3.14 for pi.
.
.
.
Question content area top right
Part 1
30 ft
30 ft
10 ft
5 ft
Question content area bottom
Part 1
The cost of the sod is approximately $
enter your response here.
(Round to the nearest cent as needed.)
.
.
.
Question content area top right
Part 1
30 ft
30 ft
10 ft
5 ft
Question content area bottom
Part 1
The cost of the sod is approximately $
enter your response here.
(Round to the nearest cent as needed.)
Answers
GPT-4o mini
To find the cost of sod for the playing field, we first need to determine the area of the field. Based on the dimensions you've provided, let’s break down the field:
1. **Rectangular Section**: The dimensions are given as 30 ft by 10 ft. The area of this rectangle is:
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 30 \, \text{ft} \times 10 \, \text{ft} = 300 \, \text{ft}^2.
\]
2. **Circular Section**: The circular area has a radius of 5 ft (since the diameter is 10 ft). The area of the circle can be calculated using the formula:
\[
\text{Area}_{\text{circle}} = \pi r^2 = 3.14 \times (5 \, \text{ft})^2 = 3.14 \times 25 \, \text{ft}^2 = 78.5 \, \text{ft}^2.
\]
3. **Total Area**: Now we find the total area of the playing field by adding the areas of the rectangle and the circle:
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{circle}} = 300 \, \text{ft}^2 + 78.5 \, \text{ft}^2 = 378.5 \, \text{ft}^2.
\]
4. **Cost of the Sod**: Next, we calculate the cost of sod at $1.74 per square foot:
\[
\text{Cost} = \text{Total Area} \times \text{Cost per square foot} = 378.5 \, \text{ft}^2 \times 1.74 \, \text{dollars/ft}^2 = 658.59 \, \text{dollars}.
\]
5. **Final Cost**: Rounding the cost to the nearest cent, the total cost of the sod is approximately:
\[
\text{Cost of the sod} \approx 658.59.
\]
Hence, the final answer is:
\[
\text{The cost of the sod is approximately } \$658.59.
\]
1. **Rectangular Section**: The dimensions are given as 30 ft by 10 ft. The area of this rectangle is:
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width} = 30 \, \text{ft} \times 10 \, \text{ft} = 300 \, \text{ft}^2.
\]
2. **Circular Section**: The circular area has a radius of 5 ft (since the diameter is 10 ft). The area of the circle can be calculated using the formula:
\[
\text{Area}_{\text{circle}} = \pi r^2 = 3.14 \times (5 \, \text{ft})^2 = 3.14 \times 25 \, \text{ft}^2 = 78.5 \, \text{ft}^2.
\]
3. **Total Area**: Now we find the total area of the playing field by adding the areas of the rectangle and the circle:
\[
\text{Total Area} = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{circle}} = 300 \, \text{ft}^2 + 78.5 \, \text{ft}^2 = 378.5 \, \text{ft}^2.
\]
4. **Cost of the Sod**: Next, we calculate the cost of sod at $1.74 per square foot:
\[
\text{Cost} = \text{Total Area} \times \text{Cost per square foot} = 378.5 \, \text{ft}^2 \times 1.74 \, \text{dollars/ft}^2 = 658.59 \, \text{dollars}.
\]
5. **Final Cost**: Rounding the cost to the nearest cent, the total cost of the sod is approximately:
\[
\text{Cost of the sod} \approx 658.59.
\]
Hence, the final answer is:
\[
\text{The cost of the sod is approximately } \$658.59.
\]