To find the volume of the movie theater, which is a composite structure made up of one large square prism and four smaller square prisms, we can calculate the volume of each part separately and then add them together.
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Volume of the large square prism:
- The formula for the volume of a square prism is: \[ V = \text{Base Area} \times \text{Height} \]
- The base area (A) of the large square prism, which has sides measuring 44 meters: \[ A = \text{side}^2 = 44^2 = 1936 \text{ m}^2 \]
- The volume of the large square prism (with height 20 meters): \[ V_{\text{large}} = 1936 \times 20 = 38720 \text{ m}^3 \]
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Volume of one small square prism:
- Each smaller square prism has sides measuring 15 meters: \[ A_{\text{small}} = \text{side}^2 = 15^2 = 225 \text{ m}^2 \]
- The height of each smaller prism is taken to be the same as the height of the large prism, which is also 20 meters: \[ V_{\text{small}} = 225 \times 20 = 4500 \text{ m}^3 \]
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Volume of all four smaller square prisms:
- Since there are four smaller square prisms: \[ V_{\text{total small}} = 4 \times V_{\text{small}} = 4 \times 4500 = 18000 \text{ m}^3 \]
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Total volume of the movie theater:
- Now we add the volume of the large square prism and the total volume of the smaller prisms: \[ V_{\text{total}} = V_{\text{large}} + V_{\text{total small}} = 38720 + 18000 = 56720 \text{ m}^3 \]
Therefore, the total volume of the movie theater is 56720 m³.