Chapter 1, Problem 29P

To determine

A rough estimate of the volume of a human body in ${\text{cm}}^3$ .

Answer to Problem 29P

The volume of a human body is approximately ${\text{10}}^5{\text{ cm}}^3$ .

Explanation of Solution

Introduction:

Method:1

Assuming a human body to be a rectangular cuboid, its length, width and thickness is determined. The volume of the human being can be determined using the formula for the volume of the cuboid.

Method:2

Using the fact that 75%of a human body is water, the density of a human body can be estimated. The volume of a body is given by,

  $\text{Volume}=\frac{\text{Mass}}{\text{Density}}$

Method:1

Assume the following measurements for a human:

  $\begin{array}{c}\text{Height}=170\text{ cm}\\ \text{Width}=36\text{ cm}\\ \text{Thickness}=10\text{ cm}\end{array}$

Calculate the volume using the expression,

  $\begin{array}{c}\text{Volume}=\text{Height}\times \text{Width}\times \text{Thickness}\\ =\left(170\text{ cm}\right)\left(36\text{ cm}\right)\left(10\text{ cm}\right)\\ =6.12\times {10}^4{\text{cm}}^3\end{array}$

This can be rounded off to the nearest power of 10 as ${\text{10}}^5{\text{ cm}}^3$ .

Method:2

Since most of the human body is made of water, it is fair to assume the density of the human body to be nearly equal to the density of water, which is $1{\text{ g/cm}}^3$ .

Taking the average mass of a human to be 65 kg, which is equivalent to $65000\text{ g}$ , the volume is calculated as follows:

  $\begin{array}{c}\text{Volume}=\frac{\text{Mass}}{\text{Density}}\\ =\frac{65000\text{ g}}{1{\text{ g/cm}}^3}\\ =6.5\times {10}^4{\text{cm}}^3\end{array}$

When rounded to the nearest power of 10, the volume is found to be ${\text{10}}^5{\text{ cm}}^3$ .

Conclusion:

Thus, the volume of a human body is approximately ${\text{10}}^5{\text{ cm}}^3$ .