Surveying Multiple Choice Questions on “Volume Measurement – Trapezoidal Formula”.
1. The trapezoidal formula can be applied only if __________
a) It composes prism and wedges
b) It composes triangles and parallelograms
c) It composes prism and parallelograms
d) It composes triangles and wedges
Answer: a
Clarification: The trapezoidal method is based on the assumption that the mid-area is the mean of the end areas. It is true only if the prismoid is composed of prisms and wedges only but not of pyramids.
2. Trapezoidal formula is also known as ____________
a) Simpson’s rule
b) Co-ordinate method
c) Prismoidal method
d) Average end area method
Answer: d
Clarification: This method is based on the assumption that the mid-area is the mean of the end areas, which make it the Average end area method.
3. Which of the following indicates the assumption assumed in the trapezoidal formula?
a) mid-area is the mean of the starting area
b) mid-area is the mean of the end area
c) mid-area is the mean
d) mid-area is not the mean of the end area
Answer: b
Clarification: Trapezoidal formula is based on the assumption that the mid-area is the mean of the end area. Based on this, the trapezoidal formula will be worked out and further calculations are done.
4. Prismoidal correction can be applied to the trapezoidal formula.
a) True
b) False
Answer: a
Clarification: Every volumetric formula needs certain corrections in order to set the errors occurred. In the case of trapezoidal formula, prismoidal corrections will be applied so as to reduce the error impact.
5. Calculate the volume of third section, if the areas are 76.32 sq. m and 24.56 sq. m with are at a distance of 4 m.
a) 210.11 cu. m
b) 201.67 cu. m
c) 201.76 cu. m
d) 210.76 cu. m
Answer: c
Clarification: Volume of the third section of a prismoid can be calculated as,
V = d/2 (A3 + A4). On substitution, we get
V = 4/2 (76.32 + 24.56)
V = 201.76 cu. m.
6. If the areas of the two sides of a prismoid represent 211.76 sq. m and 134.67 sq. m, which are 2 m distant apart, find the total volume using trapezoidal formula. Consider n=3.
a) 651.99 cu. m
b) 615.99 cu. m
c) 651.77 cu. m
d) 615.77 cu. m
Answer: d
Clarification: The total volume using trapezoidal formula can be given as,
V = d ((A1 + A2/2) + A2). On substitution, we get
V = 2 ((211.76 + 134.67/2) + 134.67)
V = 615.77 cu. m.
7. In trapezoidal formula, volume can be over estimated.
a) False
b) True
Answer: b
Clarification: Due to the consideration of mid-area of the pyramid, volume of the pyramid can be over estimated. But due to the consideration of method of end area, the over estimation can be set right.
8. Determine the volume of prismoid using trapezoidal formula, if the areas are given as 117.89 sq. m and 55.76 sq. m which are 1.5m distant apart.
a) 130.23 cu. m
b) 103.23 cu. m
c) 13.44 cu. m
d) 103.65 cu. m
Answer: a
Clarification: The volume of prismoid in case of trapezoidal formula can be given as,
V = d/2 (A1 + A2). On substitution, we get
V = 1.5/2 (117.89 + 55.76)
V = 130.23 cu. m.
9. Which of the following methods is capable of providing sufficient accuracy?
a) Area by planimeter
b) Area by co-ordinates
c) Prismoidal method
d) Trapezoidal method
Answer: d
Clarification: Trapezoidal method involves the calculation of the volume of the prismoid and the shape acquired by the traverse. During volume calculations, many methods can be employed off which the trapezoidal method is capable of delivering the utmost accuracy.
10. The correction applied in trapezoidal formula is equal to____________
a) Product of calculated volume and obtained volume
b) Summation between calculated volume and obtained volume
c) Difference between calculated volume and obtained volume
d) Division of calculated volume and obtained volume
Answer: c
Clarification: Correction applied in case of the trapezoidal formula is equal to the difference between the volume calculated and that obtained from the prismoidal formula. In general, this correction is known as prismoidal correction and can be applied to the trapezoidal formula.