How to Calculate Volume of a Lake Using Different Approximation Methods?

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To calculate the volume of a lake using the provided depth and interval data, it's essential to incorporate the third dimension, which is the lake's width or length in the z direction. The discussion highlights methods for calculating the area under the curve, such as upper and lower rectangles, the trapezium method, and Simpson's method, but emphasizes that without z-direction data, volume cannot be accurately determined. Participants express confusion regarding how to proceed without this crucial information. The lack of z-direction data is a significant barrier to calculating the lake's volume. Understanding all three dimensions is necessary for accurate volume calculations.
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I am given a table of values to calculate the volume of water in a lake.

X(m) 0 50 100 150 200 250 300
Y(m) 10.2 39.1 56.9 43.2 28.5 17.7 9.8

Where X is intervals across the lake
Where Y is depth of the lake in meters

The aim is to work out the volume using a range of different methods, including;

Upper and lower rectangles
Trapezium Method
Simpson's Method

I understand how to calculate the area under the curve, however i am not sure how to use the values calculated for area to determine the volume of the lake

Thanks
 
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I'm not sure either. Are you given any information about the z direction? You can't calculate volume if you only have information about 2 of the 3 dimensions.
 
no z direction, nothing, that is what has me confused
 
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