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?
pls
To find the volume of the movie theater, we need to first calculate the volume of the large square prism in the center and then the volume of the four smaller square prisms attached to it.
Volume of the large square prism:
Volume = area of base x height
Volume = (44m x 44m) x 20m
Volume = 19360m^2 x 20m
Volume = 387200m^3
Volume of each smaller square prism:
Volume = area of base x height
Volume = (15m x 15m) x 20m
Volume = 225m^2 x 20m
Volume = 4500m^3
Since there are four smaller square prisms attached to the large square prism, the total volume of the movie theater is:
Total Volume = Volume of large square prism + (4 x Volume of smaller square prism)
Total Volume = 387200m^3 + (4 x 4500m^3)
Total Volume = 387200m^3 + 18000m^3
Total Volume = 405200m^3
Therefore, the volume of the movie theater is 405200 cubic meters.