Volume Unit Test
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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 first need to find the volume of the large square prism in the center and then add the volume of the four smaller square prisms attached to it.
1. Volume of the large square prism in the center:
Volume = base area × height
Base area = side × side = 44m × 44m = 1936m^2
Volume = 1936m^2 × 20m = 38720m^3
2. Volume of one of the smaller square prisms:
Volume = base area × height
Base area = side × side = 15m × 15m = 225m^2
Volume = 225m^2 × 20m = 4500m^3
Since there are four smaller square prisms, we need to multiply the volume of one by 4:
Total volume of the four smaller square prisms = 4500m^3 × 4 = 18000m^3
Therefore, the total volume of the movie theater is:
Large square prism volume + Total volume of the four smaller square prisms
= 38720m^3 + 18000m^3
= 56720m^3
So, the volume of the movie theater is 56720m^3.