In the average end area method, volume is calculated as which formula?

• A. Volume = (Area1 + Area2) / 2 × spacing.
• B. Volume = Area1 × Area2 × spacing.
• C. Volume = Area1 × spacing.
• D. Volume = (Area1 + Area2) × spacing.

Answer: (A)

The main idea is that the volume of earth between two cross-sections is estimated by taking the average of the end cross-sectional areas and multiplying by the distance between those sections. This uses the trapezoidal approach to approximate how the area changes along the length.

So the volume is calculated as (A1 + A2) / 2 × spacing. This reflects averaging the end areas and extending that average across the length between them.

For example, if A1 is 100 ft^2, A2 is 140 ft^2, and the spacing is 20 ft, the volume would be ((100 + 140) / 2) × 20 = (240 / 2) × 20 = 120 × 20 = 2,400 ft^3.

Other formulas don’t fit because they mix or omit the averaging step: multiplying A1 by A2 mixes two areas in a way that has no meaningful unit or geometric interpretation; using A1 × spacing assumes the area stays the same as A1 along the length; and using (A1 + A2) × spacing would overestimate by omitting the division by 2.