chem math question

Question

1) A certain person had a brain that weighed 1.40 kg and contained 1.74 × 10¹⁰ cells. Assuming that each cell was completely filled with water (density = 1.00 g/mL), calculate the length of one side of such a cell if it were a cube. Answer in cm.

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 one side of the cell layer? Answer in m^2.

Answer 1

1.40kg = 1.4E3 g

V(brain) = 1.4E3 g / 1.00 g/mL = 1.40E3 mL = 1.40E3 cm^3

nCells = 1.74E10

V(cell) = 1.40E3 cm^3 / 1.74E10 = 8.05E-8 cm^3

L(cell) = (V(cell))^(1/3) = 4.32E-3 cm

A(cells) = L(cell) ^ 2 * nCells = (4.32E-3 cm) ^ 2 * 1.74E10 = 325E3 cm^2 = 32.5 m^2