The Correct Prismoidal Formula for Volume is

By Aina Parasher|Updated : July 7th, 2022

The correct prismoidal formula for volume is-

  1. D [first area + last area + ∑ Even area + 2 ∑ odd areas]
  2. D/3[first area + last area + 4 ∑ Even area + 2 ∑ odd areas]
  3. D/3[first area + last area + 2 ∑ Even area + 4 ∑ odd areas]
  4. D/6[first area + last area + 2 ∑ Even area + 4 ∑ odd areas]

Answer: B. D/3 [first area + last area + 4 ∑ Even area + 2 ∑ odd areas]

The correct prismoidal formula for volume is D/3 [first area + last area + 4 ∑ Even area + 2 ∑ odd areas].

Solution

 The volume calculated by the prismoidal formula is based on the Simson’s 1\3rd rule. It is the most accurate method of calculating the volume. But to calculate the volume, the Trapezoidal method is mostly used. The difference of volume by both the formulas is known as a prismoidal correction. Hence, the correct prismoidal formula for volume is-

D/3 [first area + last area + 4 ∑ Even area + 2 ∑ odd areas].

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