Volume of a section of a sphere

Question

A section of a sphere is described by $0 ≤ ≤ 2$, $0 ≤ ≤ 90°$, $30° ≤ ≤ 90°$.

Now, just by using simple symmetry, I can see that the volume of this section will be less than 1/8th of the volume of a sphere with radius 2.

Volume of the section < (Volume of the sphere of radius $2$) $/$ $8$

Volume of a sphere of radius $2$ is $33.51$ according to $4/3 \pi r^3$. I solved it using differential method but my answer is more than $1/8$th of the volume. What is wrong here?

Answer 1

In the first step we are integrating

$$\int_0^2 r^2 dr=\frac13 [r^3]_0^2=\frac83$$