Quetilon 30 of 30 (1 point) I Question Attompt i of 3 A certain person had a brain that weighed 1.35 kg and contained \( 3.82 \times 10^{70} \) cells. Part 1 of 2 Assuming that each cell was completely filled with water (density \( =1.00 \frac{g}{\mathrm{~mL}} \), , calculate the length of one side of such a cell if it were a cube. Round your answer to 3 significant digits. \[ 3.27 \times 10^{-3} \mathrm{~cm} \] Part: \( 1 / 2 \) Part 2 of 2 If the cells were spread out into a thin layer that was a single cell thick, what would be the total surface area (in square meters) for the tap side of the cell layer? Round your answer to 3 significant digits. \( \square \) Try again

To find the length of one side of a cell if it were a cube, first convert the weight of the brain into grams: \( 1.35 \, \text{kg} = 1350 \, \text{g} \). Since each cell is filled with water, the total volume of cells is equal to the mass divided by the density: \[ \text{Volume} = \frac{1350 \, \text{g}}{1.00 \, \text{g/mL}} = 1350 \, \text{mL} = 1350 \, \text{cm}^3 \] Knowing there are \( 3.82 \times 10^{70} \) cells, the volume of one cell is: \[ \text{Volume of one cell} = \frac{1350 \, \text{cm}^3}{3.82 \times 10^{70}} \approx 3.54 \times 10^{-68} \, \text{cm}^3 \] If the cell is cubic, its side length \( L \) can be found using \[ L = \sqrt[3]{\text{Volume}} \approx \sqrt[3]{3.54 \times 10^{-68}} \approx 3.27 \times 10^{-3} \, \text{cm} \] Now, for the total surface area of a thin layer of these cells spread out. Each cell has 6 faces, so the surface area of one cell is \[ \text{Surface area of one cell} = 6L^2 \] Calculating the surface area for one cell using \( L \approx 3.27 \times 10^{-3} \, \text{cm} \): \[ \text{Surface area of one cell} = 6(3.27 \times 10^{-3})^2 \approx 6(1.07 \times 10^{-5}) \approx 6.42 \times 10^{-5} \, \text{cm}^2 \] Thus, the total surface area for all \( 3.82 \times 10^{70} \) cells is: \[ \text{Total surface area} = 3.82 \times 10^{70} \times 6.42 \times 10^{-5} \approx 2.45 \times 10^{66} \, \text{cm}^2 \] Converting this to square meters, where \( 1 \, \text{m}^2 = 10^{4} \, \text{cm}^2 \): \[ \text{Total surface area} \approx \frac{2.45 \times 10^{66}}{10^{4}} \approx 2.45 \times 10^{62} \, \text{m}^2 \] Feel free to round it to three significant digits to get \( 2.45 \times 10^{62} \, \text{m}^2 \) as your answer!