Concept explainers
A human brain weighs about 1 kg and contains about
Interpretation:
The length of one side of each cell if it were a cube and the surface area if cells are spread out into a thin layer are to be calculated.
Concept introduction:
Dimensional analysis is used to set up and solve a unit conversion problem using conversion factors.
Dimensional analysis is a way to convert units of measurement. In order to convert one unit to another, the relationship between those units is to be predicted. These relationships are called conversion factors.
Answer to Problem 70QP
Solution:
Explanation of Solution
Given information: The mass of the brain
The number of cells
The density of water
The mass of a brain cell is as follows:
Assume that each cell is completely filled with water.
The volume of each cell is as follows:
Assume that the cell is cubic.
The volume of a cube is as:
Here,
Rearrange the above equation to determine the length.
The length of a single cell is as:
So, the length of a single cell is
There are
A single cell thick surface area can be calculated as follows:
First, calculate the volume for total cells and then calculate the surface area.
The volume of total cells is as follows:
Substitute the values of height (equal to length) of a cell and volume of total cells in equation (1).
Hence, the surface area is
The length of one side of each cell is
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Chapter 1 Solutions
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