spherical coordinates

[A.k]

Transform the body Ω into generalized spherical coordinates.​

Ω= {1<= (x^(2))/(4)+(y^(2))/(9)+(z^(2))/(16)<= 4 }.​

This is what i got.
x = 2r cos ϕ cos ϑ
y = 3r sin ϕ cos ϑ
z = 2r sin ϑ
J = 12r2 cos ϑ
1≤ r ≤ 2
-π /2 ≤ ϕ ≤ π/2
-π /2≤ ϑ ≤ π/ 2.
IS IT CORRECT?

 

[HallsofIvy]

\(\displaystyle \frac{x^2}{4}+ \frac{y^2}{9}+ \frac{z^2}{16}= 1\)