Use the image to answer the question.
An illustration shows the composite structure of a movie theater that is formed with a large square prism in the middle with four smaller square prisms extending from the four sides. The entire structure is 20 meters in height. The square prism in the center measures 44 meters on each side. The smaller square prisms extend outward from the center of each side. The smaller square prisms are 15 meters on each side. A sign labeled Movies sits on the top of the structure.
What is the volume of the movie theater?
To find the volume of the movie theater, we need to find the volume of each individual prism and then add them together.
1. Volume of the large square prism in the center:
Volume = base area * height
Base area = side * side
Base area = 44m * 44m = 1936 square meters
Volume = 1936 square meters * 20 meters = 38,720 cubic meters
2. Volume of each of the four smaller square prisms:
Volume = base area * height
Base area = side * side
Base area = 15m * 15m = 225 square meters
Volume = 225 square meters * 20 meters = 4500 cubic meters
Since there are 4 smaller prisms, the total volume for all four would be:
4 * 4500 = 18,000 cubic meters
Now, add the volume of the large square prism to the total volume of the four smaller prisms:
38,720 cubic meters + 18,000 cubic meters = 56,720 cubic meters
Therefore, the volume of the movie theater is 56,720 cubic meters.