Chapter 3, Problem 95A

Interpretation Introduction

Interpretation : The kilograms of water needed to fill an aquarium is to be calculated.

Concept Introduction : The measure of how densely a material is packed together is called density. It is described as the mass per unit volume.

Answer to Problem 95A

The kilograms of water needed to fill an aquarium is $\text{24}\text{kg}$ .

Explanation of Solution

Given information:

The density of water is $1{\text{g/cm}}^3$ .

The room has dimensions of $40\text{cm}$ by $20\text{cm}$ by $30\text{cm}$ .

The connectivity between mass and volume is density. The formula of mass when density and volume are given:

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

To calculate the mass of water in the aquarium, first, need to find the volume of the aquarium using its dimensions.

The volume is given as:

  $\begin{array}{c}\text{Volume}=l\times b\times h\\ =40\text{cm}\times 20\text{cm}\times 30\text{cm}\\ \text{= 24000}{\text{cm}}^3\\ =2.4\times {10}^4{\text{cm}}^3\end{array}$

To calculate the mass of water, substitute the values in the mass formula:

  $\begin{array}{c}\text{Mass}\text{=}\text{Density}\times \text{Volume}\\ =\frac{1\cancel{\text{g}}}{\cancel{{\text{cm}}^3}}\times 2.4\times {10}^4\cancel{{\text{cm}}^3}\times \frac{{10}^{-3}\text{kg}}{1\cancel{\text{g}}}\left(\because 1\text{kg}\text{=}{\text{10}}^3\text{g}\right)\\ =24\text{kg}\end{array}$