Question

A human brain weighs about 1 kg and contains about 1011 cells. Assuming that each cell is completely filled with water (density = 1 g/mL), calculate the length of one side of such a cell if it were a cube. 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 1

Answer:

Step-by-step explanation:

From the information given:

a human brain weighs = 1 kg ; = 1000 grams

Number of cells = 10¹¹ cells

The density of water filled in each cell = 1 g/mL

From above;

the weight of each of the brain cell = total weight of the human brain/the number of cells

the weight of each of the brain cell = 1000/10¹¹

the weight of each of the brain cell = 1 × 10⁻⁸ grams

Now, to calculate the quantity of water in each cell; we have:

= the weight of each brain × density

= $1 \times 10^{-8} \ g \times \dfrac{1 \ mL}{1 \ g}= 1 \times 10^{-8} \ mL$

For cube; we know that

1 mL = 1 cm³

Thus:

$1 \times 10^{-8} \ mL= 1 \times 10^{-8} \ cm^3$

Recall that; the volume of a cube as well = $x^3$

where;

x = length of each sides

∴

$x^3$ = $1 \times 10^{-8} \ cm^3$

$x = \sqrt[3]{1 \times 10^{-8}}$

x = 0.0022 cm

Thus, the length of each side of the cell = 0.0022 cm

The surface area of a single cell = x²

The surface area of a single cell = (0.0022 cm)²

The surface area of a single cell = 4.84 × 10⁻⁶ cm²

Therefore, the total surface area of  is:

$1 \times 10^{11} \ cells \times \dfrac{4.84 * 10^{-6} \ cm^2}{1 \ cell}$

= $4.84 \times 10^5 cm^2$

= $5.0\times 10^5 cm^2$

= 50 m²