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?
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 extending from the four sides.
Volume of large square prism in the center:
Volume = base area x height
Base area = side x side = 44m x 44m = 1936m^2
Height = 20m
Volume = 1936m^2 x 20m = 38720m^3
Volume of one of the smaller square prisms:
Base area = side x side = 15m x 15m = 225m^2
Height = 20m
Volume = 225m^2 x 20m = 4500m^3
Total volume of the movie theater:
38720m^3 + 4(4500m^3) = 38720m^3 + 18000m^3 = 56720m^3
Therefore, the volume of the movie theater is 56,720 cubic meters.
Solve the problem. What is the volume of a rectangular pyramid with a base of 200 square meters and a height of 75 meters? Show your work.(2 points)
To find the volume of a rectangular pyramid, you use the formula:
Volume = (1/3) x base area x height
Given that the base area is 200 square meters and the height is 75 meters, the volume can be calculated as follows:
Volume = (1/3) x 200m^2 x 75m
Volume = (1/3) x 15000m^3
Volume = 5000m^3
Therefore, the volume of the rectangular pyramid is 5000 cubic meters.