## Answer :

1.

**Identify the initial conditions and constants**:

- Initial volume ([tex]\( V_i \)[/tex]): 2.00 m³

- Initial temperature ([tex]\( T_i \)[/tex]): 22.5°C

- Final temperature ([tex]\( T_f \)[/tex]): 627°C

2.

**Determine the coefficient of volume expansion for concrete**:

- From the class textbook, the coefficient of volume expansion ([tex]\( \beta \)[/tex]) is [tex]\( 3.6 \times 10^{-5} \)[/tex] [tex]\( \text{°C}^{-1} \)[/tex].

3.

**Calculate the change in temperature**:

[tex]\[ \Delta T = T_f - T_i = 627^\circ\text{C} - 22.5^\circ\text{C} = 604.5^\circ\text{C} \][/tex]

4.

**Calculate the increase in volume ([tex]\( \Delta V \)[/tex])**:

[tex]\[ \Delta V = V_i \times \beta \times \Delta T \][/tex]

Plugging in the values:

[tex]\[ \Delta V = 2.00 \, \text{m}^3 \times 3.6 \times 10^{-5} \, \text{°C}^{-1} \times 604.5\,^\circ\text{C} \][/tex]

5.

**Perform the multiplication to find the increase in volume**:

[tex]\[ \Delta V = 2.00 \times 3.6 \times 10^{-5} \times 604.5 \][/tex]

[tex]\[ \Delta V = 0.043536 \][/tex]

6.

**Round the answer to 3 significant digits**:

[tex]\[ \Delta V \approx 0.044 \][/tex]

So, the volume of the concrete block will increase by approximately 0.044 m³.