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](https://tex.z-dn.net/?f=1%20%5Ctimes%2010%5E%7B-8%7D%20%5C%20g%20%5Ctimes%20%5Cdfrac%7B1%20%5C%20mL%7D%7B1%20%20%20%5C%20g%7D%3D%201%20%5Ctimes%2010%5E%7B-8%7D%20%5C%20mL)
For cube; we know that
1 mL = 1 cm³
Thus:
![1 \times 10^{-8} \ mL= 1 \times 10^{-8} \ cm^3](https://tex.z-dn.net/?f=1%20%5Ctimes%2010%5E%7B-8%7D%20%5C%20mL%3D%20%201%20%5Ctimes%2010%5E%7B-8%7D%20%5C%20cm%5E3)
Recall that; the volume of a cube as well = ![x^3](https://tex.z-dn.net/?f=x%5E3)
where;
x = length of each sides
∴
= ![1 \times 10^{-8} \ cm^3](https://tex.z-dn.net/?f=1%20%5Ctimes%2010%5E%7B-8%7D%20%5C%20cm%5E3)
![x = \sqrt[3]{1 \times 10^{-8}}](https://tex.z-dn.net/?f=x%20%3D%20%5Csqrt%5B3%5D%7B1%20%5Ctimes%2010%5E%7B-8%7D%7D)
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}](https://tex.z-dn.net/?f=1%20%5Ctimes%2010%5E%7B11%7D%20%20%5C%20cells%20%5Ctimes%20%5Cdfrac%7B4.84%20%2A%2010%5E%7B-6%7D%20%5C%20cm%5E2%7D%7B1%20%5C%20cell%7D)
= ![4.84 \times 10^5 cm^2](https://tex.z-dn.net/?f=4.84%20%5Ctimes%2010%5E5%20cm%5E2)
= ![5.0\times 10^5 cm^2](https://tex.z-dn.net/?f=5.0%5Ctimes%2010%5E5%20cm%5E2)
= 50 m²