Answer:
1332 m³
Step-by-step explanation:
The volume of a prism is the product of its length (12 m) and the area of its base. This base is a ∩ - shape whose overall dimensions are 11 m high and 15 m wide. The "tunnel" is shown as 6 m high, but we need to calculate how wide it is.
The two "legs" are each 3 m wide, so total 6 m in width. Then the width of the "tunnel" is the difference between that and the overall width of 15 m:
tunnel width = 15 m -6 m = 9 m
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One way to compute the base area is to subtract the tunnel area from the overall area:
base area = B = (15 m)(11 m) -(9 m)(6 m) = 165 m² -54 m² = 111 m²
The volume of the prism is ...
V = Bl = (111 m²)(12 m) = 1332 m³
The volume of the prism is 1332 m³.
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