6. A box is filled with 220 cubes with a side length of \( \frac{1}{2} \) unit. What is the volume of the box in cubic units?

To find the volume of the box, we can follow these steps: 1. **Calculate the volume of one cube**: The volume \( V \) of a cube is given by the formula: \[ V = s^3 \] where \( s \) is the side length of the cube. 2. **Substitute the side length**: In this case, the side length \( s \) is \( \frac{1}{2} \) unit. Therefore, we can calculate the volume of one cube: \[ V = \left(\frac{1}{2}\right)^3 \] 3. **Calculate the volume of one cube**: \[ V = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} = \frac{1}{8} \text{ cubic units} \] 4. **Calculate the total volume of the box**: Since there are 220 cubes in the box, the total volume \( V_{total} \) of the box is: \[ V_{total} = 220 \times \frac{1}{8} \] 5. **Perform the multiplication**: \[ V_{total} = \frac{220}{8} = 27.5 \text{ cubic units} \] Thus, the volume of the box is \( 27.5 \) cubic units.