



 
We have two responses for you Darcy, The simplest way to approach an ellipsoid is as a 'stretched sphere'. You have a hemisphere (which you know the formula for) but with stretches. So your final volume for the halfellipsoid is the formula for the hemisphere with $R^3$ replaced by $a \times b \times c$! You can apply the same type of reasoning to ellipses in the plane, etc. for the area. Walter Whiteley
Volume of an ellipsoid is$\large \frac43 \times \pi \times abc$ where a,b,c are the three radii. So a is half the length, etc. So volume of a halfellipsoid is \[\frac12 \times \frac43 \times \pi \times \frac{A}{2} \frac{B}{2} c = \frac{\pi}{6} ABc \sim 0.5236 ABc\] where A is length, B width, c height. Remember, A,B are measured right across the mound, c is from the flat surface. If you're working with soil, you are probably not working to a very high accuracy, so \[\frac{\mbox{ length } \times \mbox{ width } \times \mbox{ height }}{2}\] would be a pretty good rule of thumb. Good Hunting!  


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