Question
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)
m3
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 = side length x side length x height
Volume = 44m x 44m x 20m
Volume = 38,720m3
2. Volume of each smaller square prism:
Volume = side length x side length x height
Volume = 15m x 15m x 20m
Volume = 4,500m3 (for each smaller prism)
3. Total volume of the movie theater:
Total volume = volume of large square prism + 4 x volume of smaller square prism
Total volume = 38,720m3 + 4 x 4,500m3
Total volume = 38,720m3 + 18,000m3
Total volume = 56,720m3
Therefore, the volume of the movie theater is 56,720m3.