Volume of West Hill Pond

Since I have a bathymetric map of West Hill Pond, I thought it might be interesting to calculate the volume of the pond. The formula for calculating the volume of the frustum of a pyramid is V = \frac{1}{3} h \left( A_1 + A_2 + \sqrt{A_1 A_2} \right) where h is the height of the frustum, A_1 is the base area of the top of the frustum, and A_2 is the base area of the bottom of the frustum.1 This formula can be used with bathymetric contours to approximate the volume of a water body.2 Applying the formula to the bathymetric map of West Hill Pond results in a calculated volume of 9.3 × 106 m3, or 2.5 billion gallons.

West Hill Pond WPA Bathymetry

Also available is the bathymetric contour shapefile used.

  1. Conical Frustum — from Wolfram MathWorld 

  2. Taube, Clarence M. 2000. Instructions for winter lake mapping. Chapter 12 in Schneider, James C. (ed.) 2000. Manual of fisheries survey methods II: with periodic updates. Michigan Department of Natural Resources, Fisheries Special Report 25, Ann Arbor. 

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