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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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Answer 1

To find the volume of the movie theater, we need to calculate the volumes of both the large central square prism and the four smaller square prisms connected to it.

1. Volume of the central square prism:

   • The formula for the volume of a prism is: \[ V = \text{Base Area} \times \text{Height} \]
   • For the large central square prism:
     • Side length = 44 meters
     • Height = 20 meters
   • The base area (A) of the square prism is: \[ A = \text{side}^2 = 44^2 = 1936 \text{ m}^2 \]
   • So, the volume (V) of the central square prism is: \[ V = 1936 \times 20 = 38720 \text{ m}^3 \]

2. Volume of the smaller square prisms:

   • Each of the smaller square prisms has:
     • Side length = 15 meters
     • Height = 20 meters
   • The base area of a smaller square prism is: \[ A = \text{side}^2 = 15^2 = 225 \text{ m}^2 \]
   • So, the volume of one smaller square prism is: \[ V = 225 \times 20 = 4500 \text{ m}^3 \]
   • Since there are four smaller square prisms, the total volume for all four is: \[ 4 \times 4500 = 18000 \text{ m}^3 \]

3. Total volume of the movie theater:

   • To find the total volume of the movie theater, we add the volume of the central prism and the volume of the smaller prisms: \[ \text{Total Volume} = V_{\text{central}} + V_{\text{smaller}} = 38720 + 18000 = 56720 \text{ m}^3 \]

Thus, the total volume of the movie theater is 56720 m³.