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Trapezoidal formula is also known as _____
- a)Simpson’s rule
- b)Co-ordinate method
- c)Prismoidal method
- d)Average end area method
Correct answer is option 'D'. Can you explain this answer?
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Trapezoidal formula is also known as _____a)Simpson’s ruleb)Co-o...
Understanding the Trapezoidal Formula
The trapezoidal formula is a numerical method used for estimating the area under a curve. In civil engineering, it is particularly useful for calculating volumes of earthwork and other applications involving irregular shapes.
Correct Answer: Average End Area Method
The trapezoidal formula is often referred to as the Average End Area Method. Here's why:
Comparison with Other Methods
- Simpson’s Rule: This is another numerical integration method, but it uses quadratic functions to estimate areas, making it more accurate for certain datasets.
- Prismoidal Method: This method is similar but considers the shape of the object and is used for more complex volumes.
- Coordinate Method: This involves plotting points on a graph to find areas but is less common for volume calculations in civil engineering.
In summary, the trapezoidal formula's designation as the Average End Area Method highlights its practical utility in civil engineering for volume estimation, particularly in earthwork calculations.
The trapezoidal formula is a numerical method used for estimating the area under a curve. In civil engineering, it is particularly useful for calculating volumes of earthwork and other applications involving irregular shapes.
Correct Answer: Average End Area Method
The trapezoidal formula is often referred to as the Average End Area Method. Here's why:
- Definition: The Average End Area Method calculates the volume of a prismatic shape by taking the average of the areas at the two ends and multiplying it by the length between them.
- Application: This method is used in land surveying and civil engineering to determine the volume of cut and fill operations. It simplifies calculations for irregular cross-sections by approximating them as trapezoids.
- Methodology: The area of each cross-section is calculated using the trapezoidal formula, which is then averaged with the adjacent cross-section before multiplying by the distance between them to find the volume.
- Benefits: The Average End Area Method is efficient and provides a reasonable approximation for volumes, making it a preferred choice in field applications where precision is balanced with practicality.
Comparison with Other Methods
- Simpson’s Rule: This is another numerical integration method, but it uses quadratic functions to estimate areas, making it more accurate for certain datasets.
- Prismoidal Method: This method is similar but considers the shape of the object and is used for more complex volumes.
- Coordinate Method: This involves plotting points on a graph to find areas but is less common for volume calculations in civil engineering.
In summary, the trapezoidal formula's designation as the Average End Area Method highlights its practical utility in civil engineering for volume estimation, particularly in earthwork calculations.
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Trapezoidal formula is also known as _____a)Simpson’s ruleb)Co-o...
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.
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Trapezoidal formula is also known as _____a)Simpson’s ruleb)Co-ordinate methodc)Prismoidal methodd)Average end area methodCorrect answer is option 'D'. Can you explain this answer?
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