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

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SUMMARY

The discussion focuses on calculating the volume of a lake using provided depth values at specific intervals. The methods discussed include Upper and Lower Rectangles, the Trapezium Method, and Simpson's Method for area approximation. However, participants highlight the necessity of a third dimension (z-direction) to accurately compute volume, as volume calculation requires depth, width, and length. Without z-direction data, the volume cannot be determined from the given two-dimensional data alone.

PREREQUISITES
  • Understanding of numerical integration methods such as Upper and Lower Rectangles
  • Familiarity with the Trapezium Method for area approximation
  • Knowledge of Simpson's Method for calculating areas under curves
  • Basic principles of three-dimensional geometry and volume calculation
NEXT STEPS
  • Research the application of the Trapezium Method in volume calculations
  • Learn about the integration of depth data to derive volume in three dimensions
  • Explore numerical methods for approximating volumes of irregular shapes
  • Study the implications of missing dimensions in geometric calculations
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Students and professionals in mathematics, engineering, and environmental science who are involved in hydrology, volume calculations, and numerical methods for area approximation.

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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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