Question

A certain person had a brain that weighed 1.15 kg and contained 6.94 × 10^10

cells.
Assuming that each cell was completely filled with water (density = 1.00
-), calculate the length of one side of such a cell if it were a cube. Be sure mL
your answer has the correct number of significant digits.

Answer 1

To find the length of one side of a cell, divide the mass of the brain by the number of cells and equate it to the volume of the cell multiplied by the density of water. The length of one side of such a cell is approximately 3.029 × 10^-6 m.

Step-by-step explanation:

To find the length of one side of a cell, we can use the formula for volume. The formula for volume of a cube is V = s^3, where s is the length of a side. Given that the brain weighs 1.15 kg and contains 6.94 × 10^10 cells, we can calculate the mass of one cell by dividing the brain mass by the number of cells: 1.15 kg / (6.94 × 10^10 cells). Since each cell is completely filled with water, we can equate the mass of the cell to the volume of the cell multiplied by the density of water.

Thus, we have: mass of cell = (s^3) x (density of water). Rearranging the equation, we get: s^3 = mass of cell / (density of water). Substituting the known values, we have: s^3 = (1.15 kg / (6.94 × 10^10 cells)) / (1000 kg/m³). Evaluating this expression, we get the value of s as approximately 0.000003029 m, which can be written in scientific notation as 3.029 × 10^-6 m.