Question

Determine the density of a cylindrical solid with a mass of 19.8 g, a diameter of 9.5 mm, and a length of 20.8 mm in g/cm3. Pi = 3.14ROUND ANSWER TO ONE DECIMAL PLACE.

Answer 1

gDensity is a property of matter that relates the mass to its volume, we can calculate it with the following equation:

$\rho=\frac{M}{V}$

Where,

$\begin{gathered} \rho\text{ is the density of the substance} \\ M\text{ is the mass of the substance}=19.8g \\ \text{V is the volumen of the substance} \end{gathered}$

Now, we have to calculate the volume of the solid. We do that by calculating the volume of a cylinder. The equation is:

$V=\pi\times r^2\times h$

Where,

Pi=3.14

r= Radius = Diameter/2 = 9.5mm/2=4.75mm =0.475cm

h = Length = 20.8mm = 2.08cm

We replace the values:

$\begin{gathered} V=\pi\times(0.475\operatorname{cm})^2\times2.08\operatorname{cm} \\ V=1.47\operatorname{cm}^3 \end{gathered}$

Now, we replace the known values in the density equation:

$\rho=\frac{M}{V}=\frac{19.8g}{1.47\operatorname{cm}^3}=13.4\frac{g}{cm^3}$

So, the density of a cylindrical solid with a mass of 19.8g is 13.4g