To find the volume of the movie theater, we need to first find the volume of the larger square prism in the center and then add the volumes of the four smaller square prisms extending from the sides.
Volume of the larger square prism:
Volume = side length x side length x height
Volume = 44m x 44m x 20m
Volume = 38,720 m^3
Volume of one smaller square prism:
Volume = side length x side length x height
Volume = 15m x 15m x 20m
Volume = 4,500 m^3
Since there are four smaller square prisms, we can calculate the total volume by adding the volume of the larger square prism and the volume of the four smaller square prisms:
Total volume = 38,720 m^3 + 4(4,500 m^3)
Total volume = 38,720 m^3 + 18,000 m^3
Total volume = 56,720 m^3
Therefore, the volume of the movie theater is 56,720 cubic meters.
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
1 answer