# A block of lead, with dimensions 2.0 dm x 8.0 cm x 35 mm, has a mass of 6.356 kg. How do you calculate the density of lead in g/(cm^3)?

May 13, 2018

${\text{11.35 g/cm}}^{3}$

#### Explanation:

• Length $\text{= 2.0 dm = 20 cm}$
• Breadth $\text{= 8.0 cm}$
• Height $\text{= 35 mm = 3.5 cm}$

Volume of block

${\text{V = ℓ · b · h = 20 cm × 8.0 cm × 3.5 cm = 560 cm}}^{3}$

${\text{Density" = "Mass"/"Volume" = "6356 g"/("560 cm"^3) = "11.35 g/cm}}^{3}$

May 13, 2018

$11.35 \frac{g}{c {m}^{3}}$

#### Explanation:

So first, density = (mass)/(volume

Starting with the volume portion, we need to have all of our units in $c m$ since that's what the question asks for

$1 \mathrm{dm} = 10 c m$

$2.0 \cancel{\mathrm{dm}}$ x (10cm)/(1cancel(dm) = $20 c m$

The $8.0$ is already in $c m$ so we don't need to do anything, however, we need to convert the $35 m m$

$1 m m$ = $0.1 c m$
35cancel(mm x (0.1cm)/(1cancel(mm) = $3.5 c m$

Now we can calculate the volume using $c m$ and multiply all of our dimensions

$V o l u m e$ = $L$ x $W$ x $H$

$V$ = $20 c m$ x $8.0 c m$ x $3.5 c m$
$V$ = $560 c {m}^{3}$

Now the mass portion, we need our units in grams ($g$)

Convert $k g$ to $g$

$1 k g$ = $1000 g$

$6.356 \cancel{k g}$ x (1000g)/(1cancel(kg) = $6356 g$

So now we divide $6356 g$ by $560 c {m}^{3}$ to get our answer

$\frac{6356 g}{560 c {m}^{3}}$ = $11.35 \frac{g}{c {m}^{3}}$