A bulinding is in the form of a cylinder surmounted by a hemispherical valuted dome and contains `41(19)/(21)m^(3)` of air. If the internal diameter of dome is equal to its total height above the floor, find the height of the bulinding ?

Explanation

To solve the problem step by step, we will first analyze the structure of the building and then calculate the required height.

### Step 1: Understand the Structure
The building consists of a cylindrical part and a hemispherical dome on top. We denote the radius of both the cylinder and the dome as \( r \). The height of the cylindrical part is also equal to the radius \( r \) because the internal diameter of the dome is equal to its total height.

### Step 2: Calculate the Volume of the Building
The total volume \( V \) of the building can be expressed as the sum of the volume of the cylinder and the volume of the hemispherical dome.

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