Mathematics Asked by Buddy on December 31, 2020

Find the mass of the solid S made out of material with density f in maple.

S is a ball bounded by the sphere (x−2)^2+(y+3)^2+(z−4)^2 =5; f(x, y, z)=x^2y^2.

How can I solve without changing it into a cylindrical coordinate? I tried the following but I am not sure if I did it right.

z limit from 4-sqrt(5-(x-2)^2 -(y+3)^2) to 4+sqrt(5-(x-2)^2 -(y+3)^2)

y limit from 3-sqrt(5-(x-2)^2) to 3+sqrt(5-(x-2)^2)

and x limit from -3 to 7.

Check this for mistakes on my part...

```
restart;
VectorCalculus:-int(x^2*y^2,
[x,y,z] = Sphere(<2,-3,4>,sqrt(5)));
2320 (1/2)
---- Pi 5
7
Int(x^2*y^2,
[ z = 4-sqrt(5-(x-2)^2-(y+3)^2) .. 4+sqrt(5-(x-2)^2-(y+3)^2),
y = -3-sqrt(5-(x-2)^2) .. -3+sqrt(5-(x-2)^2),
x = 2-sqrt(5) .. 2+sqrt(5) ]):
simplify(value(%));
2320 (1/2)
---- Pi 5
7
```

Answered by acer on December 31, 2020

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