Consider that the human brain weighs about 1 kg and contains 10^11 cells. Assuming that each cell is entirely filled with water, and knowing that 1 cm^3 of water weighs 1 g, calculate the volume of a brain cell (in picoliters).
Since 1 kg = 1,000 g and 1 g = 1 cm^3, the brain is approximately 1,000 cm^3. Placing this number of the number of cells gives 10^-8 cm^3 per cell. Then convert to mL knowing that 1 cm^3 = 1 mL. Lastly, convert from mL to picoliters (10^12 pL = 10^3 mL) to obtain 10 pL.
To calculate the volume of a brain cell in picoliters, we need to convert the given information into suitable units and perform the necessary calculations. Here's how you can do it step by step:
1. Convert the weight of the brain from kilograms to grams:
- 1 kg = 1000 grams
2. Determine the weight of an individual brain cell:
- Divide the weight of the brain (in grams) by the number of cells:
- Weight of brain cell = Weight of brain / Number of cells
- Weight of brain cell = 1000 grams / 10^11 cells
3. Calculate the volume of an individual brain cell:
- Since each brain cell is entirely filled with water, the weight of the cell can be considered equal to the weight of the water it contains.
- 1 cm^3 of water weighs 1 gram, so the weight of the cell (in grams) is equal to its volume (in cm^3).
- Convert the weight of the cell from grams to picograms (10^-12 grams):
- Volume of brain cell (picoliters) = Weight of brain cell (grams) * (10^12 picoliters / 1 gram)
Now let's calculate the volume of a brain cell in picoliters:
Weight of brain cell = 1000 grams / 10^11 cells
Weight of brain cell = 10^(-8) grams
Volume of brain cell (picoliters) = 10^(-8) grams * (10^12 picoliters / 1 gram)
Volume of brain cell (picoliters) = 10^4 picoliters
Therefore, the volume of an average brain cell is approximately 10,000 picoliters.