Question
A parking garage has a tented area with a slanted roof.
A rectangular prism and a triangular prism. The rectangular prism has a length of 40 feet, width of 15 feet, and height of 20 feet. The triangular prism has a triangular base with base 20 feet and height 20 feet. The prism has a height of 40 feet.
Dimensions of the triangular prism
Base – 20 feet by 20 feet
Height – 40 feet
Dimensions of the rectangular prism
Base – 15 feet by 40 feet
Height – 20 feet
What is the total amount of volume inside the parking garage?
ft3
A rectangular prism and a triangular prism. The rectangular prism has a length of 40 feet, width of 15 feet, and height of 20 feet. The triangular prism has a triangular base with base 20 feet and height 20 feet. The prism has a height of 40 feet.
Dimensions of the triangular prism
Base – 20 feet by 20 feet
Height – 40 feet
Dimensions of the rectangular prism
Base – 15 feet by 40 feet
Height – 20 feet
What is the total amount of volume inside the parking garage?
ft3
Answers
GPT-4o mini
To find the total volume inside the parking garage, we need to calculate the volumes of both the rectangular prism and the triangular prism and then add them together.
**1. Volume of the Rectangular Prism:**
The formula for the volume \( V \) of a rectangular prism is:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
For the given rectangular prism:
- Length = 40 feet
- Width = 15 feet
- Height = 20 feet
Calculating the volume:
\[
V_{rectangular} = 40 \, \text{ft} \times 15 \, \text{ft} \times 20 \, \text{ft}
\]
\[
V_{rectangular} = 12000 \, \text{ft}^3
\]
**2. Volume of the Triangular Prism:**
The formula for the volume \( V \) of a triangular prism is:
\[
V = \text{Base Area} \times \text{Height}
\]
First, we need to calculate the area of the triangular base. The area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the triangular prism:
- Base = 20 feet
- Height of the triangle = 20 feet
- Height of the prism = 40 feet
Calculating the area of the triangular base:
\[
A = \frac{1}{2} \times 20 \, \text{ft} \times 20 \, \text{ft} = \frac{1}{2} \times 400 \, \text{ft}^2 = 200 \, \text{ft}^2
\]
Now we can calculate the volume of the triangular prism:
\[
V_{triangular} = \text{Base Area} \times \text{Height} = 200 \, \text{ft}^2 \times 40 \, \text{ft}
\]
\[
V_{triangular} = 8000 \, \text{ft}^3
\]
**3. Total Volume:**
Now we add the volumes of both prisms:
\[
\text{Total Volume} = V_{rectangular} + V_{triangular} = 12000 \, \text{ft}^3 + 8000 \, \text{ft}^3
\]
\[
\text{Total Volume} = 20000 \, \text{ft}^3
\]
Therefore, the total amount of volume inside the parking garage is **20,000 ft³**.
**1. Volume of the Rectangular Prism:**
The formula for the volume \( V \) of a rectangular prism is:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
For the given rectangular prism:
- Length = 40 feet
- Width = 15 feet
- Height = 20 feet
Calculating the volume:
\[
V_{rectangular} = 40 \, \text{ft} \times 15 \, \text{ft} \times 20 \, \text{ft}
\]
\[
V_{rectangular} = 12000 \, \text{ft}^3
\]
**2. Volume of the Triangular Prism:**
The formula for the volume \( V \) of a triangular prism is:
\[
V = \text{Base Area} \times \text{Height}
\]
First, we need to calculate the area of the triangular base. The area \( A \) of a triangle is given by:
\[
A = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the triangular prism:
- Base = 20 feet
- Height of the triangle = 20 feet
- Height of the prism = 40 feet
Calculating the area of the triangular base:
\[
A = \frac{1}{2} \times 20 \, \text{ft} \times 20 \, \text{ft} = \frac{1}{2} \times 400 \, \text{ft}^2 = 200 \, \text{ft}^2
\]
Now we can calculate the volume of the triangular prism:
\[
V_{triangular} = \text{Base Area} \times \text{Height} = 200 \, \text{ft}^2 \times 40 \, \text{ft}
\]
\[
V_{triangular} = 8000 \, \text{ft}^3
\]
**3. Total Volume:**
Now we add the volumes of both prisms:
\[
\text{Total Volume} = V_{rectangular} + V_{triangular} = 12000 \, \text{ft}^3 + 8000 \, \text{ft}^3
\]
\[
\text{Total Volume} = 20000 \, \text{ft}^3
\]
Therefore, the total amount of volume inside the parking garage is **20,000 ft³**.