Chapter 18, Problem 44A

A solid 5.0-kg cylinder is 10 cm tall with a radius of 3.0 cm. Show that its density is $18g/c{m}^3$.

To determine

To show: Density of cylinder is 18 g/cm³.

Explanation of Solution

Given:

Mass of cylinder, $m=5\text{kg}$

Height of cylinder, $h=10\text{cm}$

Radius of cylinder, $r=3\text{cm}$

Formula Used:

The density is given as,

  $\rho =\frac{m}{V}$

Where, $m$ is mass and $V$ is volume.

And volume of cylinder is given as,

  $V=\pi r^{2}h$

Where $r$ is radius of cylinder and $h$ is height of cylinder.

Calculation:

From the above relations, the density of cylinder is

  $\begin{array}{c}\rho =\frac{m}{\pi r^{2}h}\\ =\frac{5\times {10}^3\text{g}}{\pi \times {\left(3\text{cm}\right)}^2\times \left(10\text{cm}\right)}\\ \rho =17.68{\text{g/cm}}^3\\ \approx 18{\text{g/cm}}^3\end{array}$

Conclusion:

Therefore, it is proved that the density of cylinder is approximately $\rho =18{\text{g/cm}}^3$ .