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?
(1 point)
To find the volume of the movie theater, we need to calculate the volume of the large square prism in the center and then add the volume of the four smaller square prisms attached to it.
Volume of the large square prism in the center:
Volume = length x width x height
Volume = 44m x 44m x 20m
Volume = 38,720 cubic meters
Volume of one smaller square prism:
Volume = length x width x height
Volume = 15m x 15m x 20m
Volume = 4,500 cubic meters
Since there are four smaller square prisms attached to the large one, their total volume is:
Total volume of smaller square prisms = 4 x 4,500 cubic meters
Total volume of smaller square prisms = 18,000 cubic meters
Therefore, the total volume of the movie theater is the sum of the volume of the large square prism and the total volume of the smaller square prisms:
Total volume = 38,720 cubic meters + 18,000 cubic meters
Total volume = 56,720 cubic meters
So, the volume of the movie theater is 56,720 cubic meters.