For computing the volume of a prismatoid (solid with two parallel plane ends), the prismoidal formula gives a more accurate result than the trapezoidal rule because it:
Choose the correct answer
Uses more cross-sections
Accounts for the curvature of the solid by including the middle cross-section area in the formula V = L(A1 + 4Am + A2)/6
Uses only one cross-section
Ignores the end areas
Correct Answer
B. Accounts for the curvature of the solid by including the middle cross-section area in the formula V = L(A1 + 4Am + A2)/6
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Prismoidal formula: V = L(A1 + 4Am + A2)/6, where Am = area at the midpoint. This is exact for prismatoids (solids with cross-sections that are linear functions of position). It is more accurate than the trapezoidal rule (V = L(A1+A2)/2) for earthwork with curved surfaces. The prismoidal correction = L(c1-c2)(h1-h2)/12 for trapezoidal sections.
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