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?

Answer 1

To calculate the total volume of the corner store, we need to find the volume of both rectangular prisms and then sum them up.

**1. Volume of the Horizontal Rectangular Prism (the longer part)**:
- Length = 30 meters
- Width = 6 meters
- Height = 9 meters

\[
\text{Volume}_{\text{horizontal}} = \text{Length} \times \text{Width} \times \text{Height}
\]
\[
\text{Volume}_{\text{horizontal}} = 30 \, \text{m} \times 6 \, \text{m} \times 9 \, \text{m}
\]
\[
\text{Volume}_{\text{horizontal}} = 1620 \, \text{m}^3
\]

**2. Volume of the Smaller Perpendicular Rectangular Prism**:
- Length = 21 meters (as stated)
- Width = 6 meters (the same as the horizontal prism)
- Height = 9 meters

\[
\text{Volume}_{\text{perpendicular}} = \text{Length} \times \text{Width} \times \text{Height}
\]
\[
\text{Volume}_{\text{perpendicular}} = 21 \, \text{m} \times 6 \, \text{m} \times 9 \, \text{m}
\]
\[
\text{Volume}_{\text{perpendicular}} = 1134 \, \text{m}^3
\]

**3. Total Volume of the Corner Store**:
Now, we add the volumes of both the horizontal and perpendicular prisms:

\[
\text{Total Volume} = \text{Volume}_{\text{horizontal}} + \text{Volume}_{\text{perpendicular}}
\]
\[
\text{Total Volume} = 1620 \, \text{m}^3 + 1134 \, \text{m}^3
\]
\[
\text{Total Volume} = 2754 \, \text{m}^3
\]

Thus, the total volume of the corner store is **2754 cubic meters**.