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

[Endorser]

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

 

[ideasrule]

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.

 

[Endorser]

no z direction, nothing, that is what has me confused