Chapter 3, Problem 91A

Interpretation Introduction

Interpretation : The density of olive oil is to be calculated.

Concept Introduction : The connectivity between mass and volume is density. The formula of density is given as:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

The formula of volume is given as:

  $\text{Volume}=\text{length×width×height}$

Answer to Problem 91A

The density of olive oil in kilograms per liter is $\text{0}\text{.92}\text{kg/L}$ .

Explanation of Solution

Given information :

The length is $28.6\text{cm}$ .

The width is $73.0\text{mm}$ .

The height is $0.72\text{m}$ .

The mass of oil in the tank is $1.38\times {10}^4\text{g}$ .

Density is defined as the ratio of mass to volume. It gives the connectivity between mass and volume.

The formula of density is given as:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

The formula of volume is given as:

  $\text{Volume}=\text{length×width×height}$

To calculate the volume, substitute the values in the volume formula.

  $\begin{array}{c}\text{Volume}=\text{length×width×height}\\ =28.6\text{cm}\times \left(73.0\cancel{\text{mm}}\times \frac{{10}^{-1}\text{cm}}{1\cancel{\text{mm}}}\right)\times \left(0.72\cancel{\text{m}}\times \frac{{10}^2\text{cm}}{1\cancel{\text{m}}}\right)\\ =1.50\times {10}^4{\text{cm}}^3\end{array}$

To calculate the density, substitute the values in the density formula.

  $\begin{array}{c}\text{Density =}\frac{\text{mass}}{\text{volume}}\\ =\frac{1.38\times {10}^4\cancel{\text{g}}}{1.50\times {10}^4\cancel{{\text{cm}}^3}}\left(\frac{1\text{kg}}{{10}^3\cancel{\text{g}}}\right)\left(\frac{10\cancel{{\text{cm}}^3}}{1\text{L}}\right)\\ =0.92\text{kg/L}\end{array}$

Conclusion

The density of olive oil in kilograms per liter is $\text{0}\text{.92}\text{kg/L}$ .