Question
Use the image to answer the question.
An illustration shows a structure of a building shaped like an inverted letter upper L, formed by two rectangular perpendicular prisms to look like a two-winged building. The structure is 9 meters high. The horizontal rectangular prism has an overall length of 30 meters along the back edge. It has a width of 6 meters. Doors are drawn along the inside 24-meter length. The smaller perpendicular rectangular prism adjoins the horizontal prism along the right side and extends forward. It shows an inner length of 21 meters.
What is the total volume of this corner store?
m3
An illustration shows a structure of a building shaped like an inverted letter upper L, formed by two rectangular perpendicular prisms to look like a two-winged building. The structure is 9 meters high. The horizontal rectangular prism has an overall length of 30 meters along the back edge. It has a width of 6 meters. Doors are drawn along the inside 24-meter length. The smaller perpendicular rectangular prism adjoins the horizontal prism along the right side and extends forward. It shows an inner length of 21 meters.
What is the total volume of this corner store?
m3
Answers
GPT-4o mini
To find the total volume of the corner store shaped like an inverted L, we need to calculate the volume of both rectangular prisms and then add them together.
1. **Volume of the horizontal rectangular prism:**
- Length = 30 meters
- Width = 6 meters
- Height = 9 meters
The volume \( V \) of a rectangular prism is calculated by the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
Thus, the volume of the horizontal prism is:
\[
V_1 = 30 \, \text{m} \times 6 \, \text{m} \times 9 \, \text{m} = 1620 \, \text{m}^3
\]
2. **Volume of the smaller perpendicular rectangular prism:**
- Length = 21 meters (inner length from the illustration)
- Width = 6 meters (same as the horizontal prism)
- Height = 9 meters (same as the horizontal prism)
The volume of the smaller prism is:
\[
V_2 = 21 \, \text{m} \times 6 \, \text{m} \times 9 \, \text{m} = 1134 \, \text{m}^3
\]
3. **Total volume of the store:**
Now, we add the volumes of both prisms together:
\[
V_{\text{total}} = V_1 + V_2 = 1620 \, \text{m}^3 + 1134 \, \text{m}^3 = 2754 \, \text{m}^3
\]
Therefore, the total volume of the corner store is **2754 m³**.
1. **Volume of the horizontal rectangular prism:**
- Length = 30 meters
- Width = 6 meters
- Height = 9 meters
The volume \( V \) of a rectangular prism is calculated by the formula:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
Thus, the volume of the horizontal prism is:
\[
V_1 = 30 \, \text{m} \times 6 \, \text{m} \times 9 \, \text{m} = 1620 \, \text{m}^3
\]
2. **Volume of the smaller perpendicular rectangular prism:**
- Length = 21 meters (inner length from the illustration)
- Width = 6 meters (same as the horizontal prism)
- Height = 9 meters (same as the horizontal prism)
The volume of the smaller prism is:
\[
V_2 = 21 \, \text{m} \times 6 \, \text{m} \times 9 \, \text{m} = 1134 \, \text{m}^3
\]
3. **Total volume of the store:**
Now, we add the volumes of both prisms together:
\[
V_{\text{total}} = V_1 + V_2 = 1620 \, \text{m}^3 + 1134 \, \text{m}^3 = 2754 \, \text{m}^3
\]
Therefore, the total volume of the corner store is **2754 m³**.