Chapter 1, Problem 87A

To determine

The approximate mass of water in kilograms to be filled in a container of a given volume.

Answer to Problem 87A

The approximate mass of water to be filled in the container of a given volume is

  $\text{286 kg}$

Explanation of Solution

Given:

A container of dimensions 1.4 m length, 0.6 m width and 34 cm depth is used to fill water

Formula Used:

The density of a substance ratio of its mass to unit volume. It is mathematically expressed as,

  $\rho =\frac{m}{V}$

Now, when this substance is being filled into a container, the volume of the container can be considered .Using density of the substance and volume of the container, the mass of the substance can be calculated as,

  $m=\rho V$

Calculation:

The substance in this case is water and density of water is $1\times {10}^3{\text{ kg/m}}^3$ . The container is of the dimensions l=1.4 m length, b=0.6 m width and h=34 cm depth. Therefore, the volume of the container is given by

  $\begin{array}{c}V=lbh\\ =1.4\times 0.6\times 0.34\\ =0.2856{\text{ m}}^3\end{array}$

Substituting the volume and density of water, the mass of water in kilograms can be calculated as,

  $\begin{array}{c}m={10}^3\times 0.2856\\ =285.6\text{ kg}\end{array}$

In terms of one significant figure, the mass in kilograms can be approximated as,

  $m\simeq 286\text{ kg}$

Conclusion:

The approximate mass of water in kilograms is 286 kg.