Calculate the volume of earthwork between two sections 40 m apart, if the mid sectional area between the sections is 15 m².
- A450 m³
- B750 m³
- C500 m³
- D600 m³Correct
Solution
Concept
In the mid-sectional area method, volume = area of the mid section × distance between the end sections.
Formula
V = Am × L
Step-by-step solution
1. Given: L = 40 m, Am = 15 m². 2. V = Am × L. 3. V = 15 × 40 = 600 m³.
Explanation
The mid-sectional area method multiplies the area at the middle section by the length between the two end sections. Here 15 m² × 40 m = 600 m³.
Why the other options are wrong
A (450), B (750) and C (500) do not equal 15 × 40. They come from wrong multiplication or wrong formula use.
Shortcut
Volume = mid area × length = 15 × 40 = 600 m³.
Common mistake
Dividing the length by 2, or using the mean-area or prismoidal formula when only the mid area is given.
Correct answer: D) 600 m³