It changes because the radius is contineously increse from top to bottom. The hight from bottom of sphere to upper surface of disk is equal to h₁ and hight from bottom of sphere to lower surface of disk is equal to h₂. Then we can find hight of disk that is (h₁ - h₂).
Now we find relation between radius of upper surface of the disk and it's hightfrom the bottom of the hemi sphere.
first we draw line from center of the hemi sphere to the most outer part of the thin circular disk. The length of this line is R.
R,r₁,h₁ makes a right angle triangle and R is hypoteneous so R² = r₁² + h₁²
Similarly R² = r₂² + h₂²

Let the mean radius of the disk from volume of prospective area of disk is equal to r_m and mean hight of the disk from of the base is equal to h_m.
now, area of disk = (22/7)r_m²
= 22/7(R² - h_m²)
Volume of disk = area of disk x hight of disk
= (22/7)r_m² x (h₁-h₂)
= 22/7(R² - h_m²) (h₁-h₂)
= (22/7)R² (h₁ -h₂)- (22/7)h_m²(h₁ - h₂)

As like this disk we cut many more small circular disk sum of all these small disk we find volume of hemi sphere. So now we write
(22/7)R²[(h₁-h₂) + (h₂-h₃)+......(h_n-1-h_n)] - (22/7)h_m²(h₁ - h₂)
(22/7)R²[(h₁- h_n)] - 3h_m²/3 (22/7)(h₁-h₂)
(22/7)R²[(h₁- h_n)] - (h₁² + h₂² +h₁ h₂)/3 (22/7)(h₁-h₂)
(22/7)R²[(h₁- h_n)] - (22/7)/3(h₁³ - h₂³)
(22/7)R²[(h₁- h_n)] - (22/7)/3[(h₁³-h₂³) + (h₂³-h₃³)+......(h_n-1³-h_n³)]
(22/7)R²[(h₁- h_n)] - (22/7)/3[(h₁³ - h_n³)]

when h_n = 0 and h₁ = R
(22/7)R²(R) - (22/7)/3 (R³)
(22/7)R³ - (22/7)/3 (R³)
[3(22/7)R³ - (22/7)R³]/3
[(22/7)R³(3-1)]/3 = 2(22/7)R³/3
Now volume of hemi sphere = [2(22/7)R³]/3 = 134.09523809524 unit