Chapter 10, Problem 4P

To determine

To Estimate: The mass of a swimmer and volume.

Answer to Problem 4P

The mass of the swimmer is considered as the average mass of person, it is $75\text{ kg}$ and then the volume of the swimmer is $75\text{ L}$ .

Explanation of Solution

Given info:

Average mass of person $m=75\text{ kg}$

Density of person = density of water= $\rho ={10}^3{\text{ kg/m}}^{\text{3}}$

Formula used:

The expression for the density.

  $\text{Density }\rho \text{ = }\frac{\text{Mass}}{\text{Volume}}\text{ = }\frac{m}{V}$

From the above expression, volume can be written as:

  $\text{Volume }V\text{ = }\frac{\text{Mass}}{\text{Density}}\text{= }\frac{m}{\rho }$

Calculation:

The average mass of the person is assumed as 75 kg.

Substitute the mass value in the volume equation,

  $V\text{ = }\frac{\text{Mass}}{\text{Density}}\text{= }\frac{75}{{10}^3}=0.075{\text{ m}}^{\text{3}}$

Now, $\text{ for }1\text{ L }={10}^{-3}{\text{m}}^{\text{3}}\text{,}$

  $0.075{\text{ m}}^{\text{3}}=75\text{L}$

So, the total volume is $75\text{ L}$ .

Conclusion:

For the mass of $75\text{ kg}$ the volume of the swimmer is $75\text{ L}$ .