Question

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)`?

Answer 1

`"11.35 g/cm"^3`

Explanation:

• Length `"= 2.0 dm = 20 cm"`
• Breadth `"= 8.0 cm"`
• Height `"= 35 mm = 3.5 cm"`

Volume of block

`"V = ℓ · b · h = 20 cm × 8.0 cm × 3.5 cm = 560 cm"^3`

Density of lead is

`"Density" = "Mass"/"Volume" = "6356 g"/("560 cm"^3) = "11.35 g/cm"^3`

Answer 2

`11.35g/(cm^3)`

Explanation:

So first, `density = (mass)/(volume`

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

`1 dm = 10 cm`

`2.0cancel(dm)` x `(10cm)/(1cancel(dm)` = `20cm`

The `8.0` is already in `cm` so we don't need to do anything, however, we need to convert the `35mm`

`1mm` = `0.1cm`
`35cancel(mm` x `(0.1cm)/(1cancel(mm)` = `3.5cm`

Now we can calculate the volume using `cm` and multiply all of our dimensions

`Volume` = `L` x `W` x `H`

`V` = `20cm` x `8.0cm` x `3.5cm`
`V` = `560cm^3`

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

Convert `kg` to `g`

`1kg` = `1000g`

`6.356cancel(kg)` x `(1000g)/(1cancel(kg)` = `6356g`

So now we divide `6356g` by `560cm^3` to get our answer

`(6356g)/(560cm^3)` = `11.35g/(cm^3)`