Prismoidal correction in surveying

Prismoidal correction is a term used in surveying to account for the errors that occur when calculating the volume of a prismoidal-shaped object. A prismoid is a three-dimensional geometric shape that has two parallel bases and four lateral faces that are trapezoids.

Prismoidal correction is necessary because when calculating the volume of a prismoid using the formula V = (A1 + A2 + √(A1 * A2))/3 * h, where A1 and A2 are the areas of the bases and h is the height, there is a discrepancy between the calculated volume and the actual volume. This discrepancy arises because the formula assumes the prismoid to be a perfect geometric shape, which is rarely the case in real-world surveying.

Subtractive correction

When applying prismoidal correction, we need to consider whether the correction should be subtractive or additive. The correct answer to the given question is option 'c', which states that the correction is subtractive. Let's understand why prismoidal correction is subtractive.

When the surveyed prismoid is compared to a perfect geometric shape, it is common for the actual volume to be less than the calculated volume. This is because the trapezoidal faces of the prismoid are not perfectly flat and straight, which leads to a smaller volume. Therefore, to correct for this discrepancy, we subtract a certain value from the calculated volume.

The subtractive correction compensates for the excess volume that is obtained by assuming a perfect geometric shape. By subtracting a value from the calculated volume, we can obtain a more accurate representation of the actual volume of the prismoid.

Conclusion

In conclusion, prismoidal correction in surveying is subtractive in nature. This correction is necessary because the calculated volume of a prismoid using a perfect geometric shape does not accurately represent the actual volume due to the real-world imperfections of the shape. Subtracting a correction value allows for a more accurate estimation of the volume of the prismoid.