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Answer 1 · 2017-05-24T01:28:25

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

The volume of a cylinder is represented by the equation

$V = π r^{2} h$ $V = pir^2h$

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

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

The volume of the cylinder is thus

$V = π {(0.25 m)}^{2} (0.75 m) = 0.15 m^{3}$ $V = pi(0.25m)^2(0.75m) = 0.15 "m"^3$

The equation for density is

$ρ = \frac{m}{V}$ $rho = m/V$

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

Density is often expressed in units of $\frac{g}{{cm}^{3}}$ $"g"/"cm"^3$ , 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 $"g"/"cm"^3$ ,

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