Quiz 3 Ordinary Double Integral

From an exploration of andesitic resource deposit, the topographical surface of andesitic deposit can be expressed using top half ellipsoid according to local coordinate (x,y,z) as:

a = 100 m (East-West half length from origin); b = 50 m (North-South half width from origin) and c = 25 m (the height at origin over the ground surface). The ground surface is averagely leveled at 0 m.asl. The unit weight of andesitic rock is about 2.6 ton/m3. Compute: andesitic rock resource above the ground surface !

Note: the basic idea is to compute the volume of top half ellipsoid!

Jawab :

Persamaan permukaan batuan andesit, dimana z = 0, a = 100, b = 50 dan c = 25 menjadi :

Untuk menghitung volume menggunakan persamaan :

Mencari batas x, jika y = 0; z = 0

Mencari batas y, jika x = 0; z = 0

Maka,

Maka, didapatkan jumlah sumberdaya sebesar : = 1.462.500 ton