A depressed portion of a land is identified by three closed contours, as shown in the figure below. The area bounded by three contour

Q. A depressed portion of a land is identified by three closed contours, as shown in the figure below. The area bounded by three contour lines are 6 m², 24 m² and 96 m² respectively. The contour interval is 1 m. Using prismoidal method, the volume of the earth needed to fill the land depression is ________________m³.

A. 66 cubic meter

B. 99 cubic meter

C. 33 cubic meter

D. 9.9 cubic meter

Ans: 9.9 cubic meter

Solution:

The volume of a prismoid is :

V = -1/6(A1 + 4Am + A2)

Where: V = Volume (cubic feet) Am = Middle Area or Area of a plane surface midway between A1 and A2, A1 and A2 are the areas of the end sections. L is distance between top and bottom cross-section.