Solution:

Let the radius of the dome be r.

Internal diameter = 2r

Given internal diameter is equal to total height.

Total height of the building = 2r

Height of the hemispherical area = r

So height of cylindrical area, h = 2r-r = r

Volume of the building = Volume of cylindrical area + volume of hemispherical area

= r²h + (2/3)r³

= r³+ (2/3)r³ [∵h = r]

= r³ (1+2/3)

= r³ (3+2)/3

= (5/3)r³

Given Volume of the building =
= 880/21

(5/3)r³= 880/21

(5/3)×(22/7)×r³= 880/21

r³ = 880×3×7/(5×22×21)

r³ = 880/110

r³ = 8

Taking cube root

r = 2 m

Height of the building = 2r = 2×2 = 4m

Hence the height of the building is 4m.