# Question 14da6

May 24, 2017

$0.81 {\text{g"/"cm}}^{3}$

#### Explanation:

The volume of a cylinder is represented by the equation

$V = \pi {r}^{2} h$

Which, if you might notice, is simply the equation for the area of a circle, $\pi {r}^{2}$, multiplied by the height, $h$.

The diameter is equal to $2 r$, so r = 1/2(0.5"m") = 0.25"m"

The volume of the cylinder is thus

$V = \pi {\left(0.25 m\right)}^{2} \left(0.75 m\right) = 0.15 {\text{m}}^{3}$

The equation for density is

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

Density is equal to the mass of the substance per unit volume.

Density is often expressed in units of ${\text{g"/"cm}}^{3}$, so let's convert our units to these:

0.15cancel("m"^3)((100^3"cm"^3)/(1cancel("m"^3))) = 1.5 xx 10^5 "cm"^3

122cancel("kg")((10^3"g")/(1cancel("kg"))) = 1.22 xx 10^5 "g"

So our density is, in ${\text{g"/"cm}}^{3}$,

rho = (1.22 xx 10^5 "g")/(1.5 xx 10^5 "cm"^3) = color(red)(0.81"g"/"cm"^3#