Use the image to answer the question.

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?

(1 point)
m3

Answer 1

To calculate the total volume of the corner store, we will find the volumes of the two rectangular prisms and then sum them.

1. Volume of the horizontal rectangular prism:

   • Length (l) = 30 meters
   • Width (w) = 6 meters
   • Height (h) = 9 meters

   Volume (V1) = l × w × h \[ V1 = 30 , \text{m} \times 6 , \text{m} \times 9 , \text{m} = 1620 , \text{m}^3 \]

2. Volume of the smaller perpendicular rectangular prism:

   • Inner Length (l) = 21 meters (this will be used as the length)
   • Width (w) = 6 meters (the same width as the horizontal prism)
   • Height (h) = 9 meters

   Volume (V2) = l × w × h \[ V2 = 21 , \text{m} \times 6 , \text{m} \times 9 , \text{m} = 1134 , \text{m}^3 \]

3. Total Volume of the Corner Store: \[ \text{Total Volume} = V1 + V2 \] \[ \text{Total Volume} = 1620 , \text{m}^3 + 1134 , \text{m}^3 = 2754 , \text{m}^3 \]

Thus, the total volume of the corner store is 2754 m³.