Earthwork Areas & Volumes Complete

Seven documents, 102 pages — every area and volume method, with solutions.

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About this course

The most complete area-and-volume collection in the academy. It moves from regular and irregular figures through the trapezoidal and Simpson's rules, coordinates and planimeters, to cross-sections and earthwork volumes — then reinforces everything with a full set of example questions and scanned, step-by-step handwritten solutions to composite-figure problems.

Regular, irregular and coordinate area methods
Cross-sections, end-area and prismoidal volumes
Example questions plus handwritten worked solutions

Syllabus

7 documents · 102 pages · English

01
Area of Regular Shapes
PDF · 5 pages
- Triangles, rectangles, trapezia and circles
- Choosing the right formula for a field figure
02
Area of Irregular Shapes
PDF · 7 pages
- The trapezoidal rule
- Simpson's rule and the odd-offset condition
- Two worked examples and a homework set
03
Volume
PDF · 10 pages
- The general rule for volumes
- The average end-area method
- Volumes from more than two sections
- Worked example
04
Topic 2 · Area & Volume
PDF · 26 pages
- Objectives and engineering uses of area and volume
- Rectilinear areas by equations, coordinates and planimeter
- Irregular areas by the trapezoidal and Simpson's rules
- Cross-sections: level, two-level and part cut / part fill
- Area by coordinates: ½ Σ E(Nᵢ₊₁ − Nᵢ₋₁)
05
Area & Volume · Illustrated Lecture Slides
PDF · 19 pages
- Digital and optical polar planimeters
- Mathematical formulae for standard figures
- Area of a closed traverse by coordinates
- Trapezoidal-rule examples from chain surveys
06
Area & Volume · Example Questions
PDF · 17 pages
- Triangle areas: Heron's formula, ½bh and ½ab sin C
- Offset areas with the trapezoidal and Simpson's rules
- DMD area from balanced departures
- Volumes by end-area and prismoidal formulas
07
Area · Worked Solutions (Scanned Notes)
PDF · 18 pages
- Composite figures combining offsets, triangles and circular segments
- Step-by-step handwritten solutions
- Summing rectilinear and irregular parts into a total area