What is the volume of a 6 m deep tank having rectangular shaped top 6 m x 4 m and bottom 4 m x 2m
(computed through the use of prismoidal formula)?
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A.
92 m³
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B.
96 m³
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C.
90 m³
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D.
94 m³
Correct Answer:
A. 92 m³
Explanation:
The volume of a tank with parallel rectangular ends can be determined using the prismoidal formula: V = (h / 6) × [A1 + A2 + 4Am]. In this case, the depth (h) is 6 m. The area of the top surface (A1) is 6 m × 4 m = 24 m2, and the area of the bottom surface (A2) is 4 m × 2 m = 8 m2. To find the area of the mid-section (Am), calculate the average dimensions: the mid-length is (6 + 4) / 2 = 5 m and the mid-width is (4 + 2) / 2 = 3 m, resulting in an area of 15 m2. Plugging these values into the formula yields V = (6 / 6) × [24 + 8 + 4(15)], which simplifies to 24 + 8 + 60, totaling 92 m3.
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