Question
The diagram below shows a doghouse that Calvino built.
1.5 ft
3.0 ft
4.5 ft
4.5 ft
What is the volume of the doghouse?
햠 15.1875 ft
3
햡 30.375 ft
3
햢 60.75 ft
3
햣 75.9375 ft
3
1.5 ft
3.0 ft
4.5 ft
4.5 ft
What is the volume of the doghouse?
햠 15.1875 ft
3
햡 30.375 ft
3
햢 60.75 ft
3
햣 75.9375 ft
3
Answers
GPT-4o mini
To calculate the volume of the doghouse that Calvino built, we first need to determine the shape of the doghouse based on the provided dimensions.
Assuming the doghouse is shaped like a rectangular prism with a triangular roof, we can calculate its volume in two parts: the volume of the rectangular base and the volume of the triangular prism (the roof).
1. **Rectangular Base Volume**:
The base is a rectangle with the dimensions:
- Width (W) = 1.5 ft
- Length (L) = 3.0 ft
- Height (H) = 4.5 ft
The volume \( V_{base} \) of the rectangular section is given by the formula:
\[
V_{base} = L \times W \times H = 3.0 \, \text{ft} \times 1.5 \, \text{ft} \times 4.5 \, \text{ft}
\]
Performing the multiplication:
\[
V_{base} = 3.0 \times 1.5 \times 4.5 = 20.25 \, \text{ft}^3
\]
2. **Triangular Roof Volume**:
The roof appears to be a triangular prism. The dimensions you provided suggest that the height of the triangular part is also equivalent to the height calculated in the rectangular base, which is 4.5 ft. The base of the triangle (the width of the doghouse) is 1.5 ft (the width of the rectangular base), and since the length of the prism matches that of the base, we will set it to 3.0 ft.
The area of the triangular face (A) is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
The base is 1.5 ft and the height of the triangle can be assumed to be the same as the width:
\[
A = \frac{1}{2} \times 1.5 \, \text{ft} \times 4.5 \, \text{ft} = \frac{1}{2} \times 6.75 \, \text{ft}^2 = 3.375 \, \text{ft}^2
\]
The volume \( V_{roof} \) of the triangular prism (the roof) is then given by:
\[
V_{roof} = A \times \text{length of prism} = 3.375 \, \text{ft}^2 \times 3.0 \, \text{ft} = 10.125 \, \text{ft}^3
\]
3. **Total Volume**:
Finally, we add the volume of the base and the volume of the roof.
\[
V_{total} = V_{base} + V_{roof} = 20.25 \, \text{ft}^3 + 10.125 \, \text{ft}^3 = 30.375 \, \text{ft}^3
\]
Thus, the volume of the doghouse is **30.375 ft³**.
The answer is: **햡 30.375 ft³**.
Assuming the doghouse is shaped like a rectangular prism with a triangular roof, we can calculate its volume in two parts: the volume of the rectangular base and the volume of the triangular prism (the roof).
1. **Rectangular Base Volume**:
The base is a rectangle with the dimensions:
- Width (W) = 1.5 ft
- Length (L) = 3.0 ft
- Height (H) = 4.5 ft
The volume \( V_{base} \) of the rectangular section is given by the formula:
\[
V_{base} = L \times W \times H = 3.0 \, \text{ft} \times 1.5 \, \text{ft} \times 4.5 \, \text{ft}
\]
Performing the multiplication:
\[
V_{base} = 3.0 \times 1.5 \times 4.5 = 20.25 \, \text{ft}^3
\]
2. **Triangular Roof Volume**:
The roof appears to be a triangular prism. The dimensions you provided suggest that the height of the triangular part is also equivalent to the height calculated in the rectangular base, which is 4.5 ft. The base of the triangle (the width of the doghouse) is 1.5 ft (the width of the rectangular base), and since the length of the prism matches that of the base, we will set it to 3.0 ft.
The area of the triangular face (A) is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
The base is 1.5 ft and the height of the triangle can be assumed to be the same as the width:
\[
A = \frac{1}{2} \times 1.5 \, \text{ft} \times 4.5 \, \text{ft} = \frac{1}{2} \times 6.75 \, \text{ft}^2 = 3.375 \, \text{ft}^2
\]
The volume \( V_{roof} \) of the triangular prism (the roof) is then given by:
\[
V_{roof} = A \times \text{length of prism} = 3.375 \, \text{ft}^2 \times 3.0 \, \text{ft} = 10.125 \, \text{ft}^3
\]
3. **Total Volume**:
Finally, we add the volume of the base and the volume of the roof.
\[
V_{total} = V_{base} + V_{roof} = 20.25 \, \text{ft}^3 + 10.125 \, \text{ft}^3 = 30.375 \, \text{ft}^3
\]
Thus, the volume of the doghouse is **30.375 ft³**.
The answer is: **햡 30.375 ft³**.