A certain person had a brain that weighed 1.25 kg and contained \( 2.49 \times 10^{10} \) cells. Part: \( 0 / 2 \) Part 1 of 2 Assuming that each cell was completely filled with water (density \( =1.00 \frac{\mathrm{~g}}{\mathrm{~mL}} \) ), calculate the length of one side of such a cell if it were a cube. Round your answer to 3 significant digits.

To find the length of one side of the cell if it were a cube, we can start by determining the volume of a single cell and then take the cube root to find the length of one side. 1. **Calculate Total Volume of Cells**: Since each cell is assumed to be filled with water, and the brain weighs 1.25 kg (or 1250 g), we can calculate the total volume of all the cells: \[ \text{Volume} = \text{mass} \div \text{density} = 1250 \, \text{g} \div 1.00 \, \text{g/mL} = 1250 \, \text{mL} \] 2. **Volume per Cell**: To find the volume of a single cell, we divide the total volume by the number of cells: \[ \text{Volume per cell} = \frac{1250 \, \text{mL}}{2.49 \times 10^{10}} \approx 5.02 \times 10^{-6} \, \text{mL} \] 3. **Convert Volume to Cubic Centimeters**: Since \(1 \, \text{mL} = 1 \, \text{cm}^3\), we can directly use the volume in cm³: \[ \text{Volume per cell} \approx 5.02 \times 10^{-6} \, \text{cm}^3 \] 4. **Calculate Length of One Side**: The volume of a cube is given by \(V = s^3\) where \(s\) is the side length. We can solve for \(s\): \[ s = \sqrt[3]{\text{Volume per cell}} = \sqrt[3]{5.02 \times 10^{-6}} \approx 1.71 \times 10^{-2} \, \text{cm} \] 5. **Convert to Millimeters**: Since 1 cm = 10 mm, we convert: \[ s \approx 1.71 \times 10^{-2} \, \text{cm} \times 10 \approx 0.171 \, \text{mm} \] Finally, rounding to three significant digits, the length of one side of such a cell is approximately: \[ \boxed{0.171 \, \text{mm}} \]