This set of Surveying Multiple Choice Questions & Answers (MCQs) focuses on “Volume Measurement – Prismoidal Formula”.
1. A prismoid is a combination of which of the following?
a) Trapezium, circle
b) Parallelogram, trapezium
c) Triangle, trapezium
d) Triangle, circle
Explanation: The longitudinal faces of the prismoid are in the form of triangle, parallelogram or trapezium. A prismoid is a solid whose end faces lies in parallel planes, which can be used for calculating the volume of the obtained figure due to surveying.
2. The trapezoidal and prismoidal formulae were derived based on the assumption that end sections are in parallel planes.
Explanation: The prismoidal and the trapezoidal formulae were derived on the assumption that the end sections are in parallel planes. So, the centre line of an embankment is curved in plan and it is common to calculate the volume as if the end sections were in parallel planes and then apply the correction for curvature.
3. Prismoidal rule is also known as__________
a) Simpson’s rule
b) Trapezoidal rule
c) Curvature rule
d) Euler’s rule
Explanation: Prismoidal rule is also known as Simpson’s rule because the formula obtained from the derivation represents the formula of Simpson’s one- third rule.
4. The prismoidal formula is used for the calculation of__________
Explanation: The calculation of volume includes the following processes trapezoidal formula, prismoidal formula which can be used for better enhancement and for obtaining accurate output.
5. Calculate the total volume if number of sides = 3 and d = 2 m. The values of area can be given as 117.98 sq. m, 276.54 sq. m and 98.43 sq. m.
a) 1170.26 cu. m
b) 1710.26 cu. m
c) 1107.26 cu. m
d) 117.26 cu. m
Explanation: The total volume of any figure can be calculated by using the Simpson’s formula i.e.,
V = d/3 (A1 + A3 + 4*A2 + 2A3 + 2A1). On substitution, we get
V = 2/3 (117.98 + 98.43 + 4*276.54 + 2*98.43 + 2*117.98)
V = 1170.26 cu. m.
6. In prisomidal rule, it is necessary to have odd number cross sections.
Explanation: It is not compulsory, but having odd number of cross sections makes the process simpler when compared to the presence of even number of cross sections.
7. Which of the following must be done for obtaining equivalent area?
a) Applying correction for bearings
b) Applying correction for angles
c) Applying correction for curvature
d) Applying correction for length
Explanation: The corrections for curvature are applied to the areas of cross-sections thus getting equivalent areas and then use them in prismoidal formula. For example, In Level section, no correction is necessary since the area is symmetrical about the central line.
8. If the area of mid section is 345.98 sq. m and the individual areas A1, A2 are 123.31 and 157.31 respectively, d = 5m. Find the volume of the pyramid.
a) 3187.11 cu. m
b) 1378.11 cu. m
c) 1837.11 cu. m
d) 1387.11 cu. m
Explanation: The volume of pyramid with lateral sides can be given as,
V = d/6 (A1+A2+4Am). On substitution, we get
V = 5/6 (123.31 + 157.31 + 4*345.98)
V = 1387.11 cu. M.
9. Which of the following indicates the formula for prisomidal correction?
a) Cp = d n (h+h1)2/6
b) Cp = d n (h-h1)2/6
c) Cp = d n (h*h1)2/6
d) Cp = d n (h/h1)2/6
Explanation: The formula for prisomidal correction is given as, Cp = d n (h-h1)2/6 which is used based on the type of work being done and accuracy of the output required.
10. Find the area of first prismoid if the areas of A1, A2 and A3 are 145.31, 257.43 and 59.67 respectively with a distance of 2.5 m.
a) 1208.91 cu. m
b) 1082.91 cu. m
c) 1028.91 cu. m
d) 1820.91 cu. m
Explanation: Volume of the first prismoid can be given as,
V = d/3 (A1 + 4*A2 + A3)
V = 2.5/3 (145.31 + 4*257.43 + 59.67)
V = 1028.91 cu. M.
Sanfoundry Global Education & Learning Series – Surveying.
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