Question

Identify the INCORRECT statement about prismoidal formula used to compute earthwork

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Prismoidal formula is also known as Simpson's rule for volume

प्रिज्मॉइडल सूत्र को आयतन के लिए सिम्पसन नियम के रूप में भी जाना जाता है

If there is an even number of cross sections, the end strip must be treated separately, and volume between the remaining sections may be calculated by prismoidal formula

यदि अनुप्रस्थ काटों की संख्या सम है, तो अंतिम पट्टी को अलग से माना जाना चाहिए, तथा शेष खंडों के बीच आयतन की गणना प्रिज्मोइडल सूत्र द्वारा की जा सकती है

It is necessary to have an odd number of cross-sections to apply prismoidal formula

प्रिज्मॉइडल सूत्र लागू करने के लिए विषम संख्या में अनुप्रस्थ-काट का होना आवश्यक है

The ratio of volume calculated by end area formula and the prismoidal formula is called as the Prismoidal correction

अंत क्षेत्र सूत्र और प्रिज्मोइडल सूत्र द्वारा गणना किए गए आयतन के अनुपात को प्रिज्मोइडल सुधार कहा जाता है

Answer ( Option D)

The ratio of volume calculated by end area formula and the prismoidal formula is called as the Prismoidal correction

Solution

Trapezoidal Formula:

• Volume (V) of earthwork between a number of sections having areas A₁, A₂, ..... , A_n spaced at a

constant distance d.

Simpson's / Prismoidal Formula:

• For irregular boundaries, Simpson's rule is preferred over the trapezoidal rule to calculate the given area.

• According to this rule the short length of boundaries between the two adjacent ordinates is a parabolic arch.

• In order to apply Simpson's rule, the area must be divided in an even number i.e., the number of offsets/areas must be odd.

• In the case of an even number of cross-sections, the end strip is treated separately and the area of the remaining strip is calculated by Simpson's rule. The area of the last strip may be calculated by trapezoidal formula

• Volume (V) of the earthwork between a number of sections having area A₁, A₂, ...... , A_n spaced at

constant distance d apart is

• The same formula can be used for finding, the storage capacity of the reservoir in terms of its volume

Prismoidal correction:

• The volume by the prismoidal formula is more accurate than any other method But the trapezoidal method is more often used for calculating the volume of earthwork in the field.

• The difference between the volume computed by the trapezoidal formula and the prismoidal formula is known as a prismoidal correction.

• Since the trapezoidal formula always overestimates the volume, the prismoidal correction is always subtractive in nature is usually more than calculated by the prismoidal formula, therefore the prismoidal correction is generally subtractive.

• Volume by prismoidal formula = volume by the trapezoidal formula – prismoidal correction