✔ 最佳答案
We may use integration of piecewise volume of triangular plates as follows:
圖片參考:
http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Doraemonapril1.jpg
Please note that △EFG is similar to △ABC if:
DE/DA = DF/DB = DG/DC
So viewing each of the side planes of the irregular tetrahedron, we have:
圖片參考:
http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Doraemonapril2.jpg
And therefore, area of △EFG (and hence its volume) can be found by Heron's formula as follows:
圖片參考:
http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Doraemonapril3.jpg
Finally, integrating from base to the vertex (i.e. x from 0 to 13), we have:
圖片參考:
http://i117.photobucket.com/albums/o61/billy_hywung/Maths/Doraemonapril4.jpg