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
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To find the volume of the movie theater, we first need to find the volume of the central prism and then add the volume of the four smaller prisms extending from the sides.
1. Volume of central prism:
Volume = (side length)^2 x height
Volume = 44^2 x 20
Volume = 19360 m^3
2. Volume of each smaller prism:
Volume = (side length)^2 x height
Volume = 15^2 x 20
Volume = 4500 m^3
3. Total volume:
Total volume = Volume of central prism + (Volume of each smaller prism x 4)
Total volume = 19360 + (4500 x 4)
Total volume = 19360 + 18000
Total volume = 37360 m^3
Therefore, the volume of the movie theater is 37360 m^3.
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, we use the formula:
Volume = (1/3) x Base Area x Height
Given:
Base Area = 200 square meters
Height = 75 meters
Plugging in the values:
Volume = (1/3) x 200 x 75
Volume = (1/3) x 15000
Volume = 5000 cubic meters
Therefore, the volume of the rectangular pyramid is 5000 cubic meters.
shorter
Volume = (1/3) x Base Area x Height
Volume = (1/3) x 200 x 75
Volume = 5000 cubic meters
Answer: 5000 cubic meters