1. The standard kilogram (Fig. 1.1a) is a platinum–iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material?
1. The standard kilogram (Fig. 1.1a) is a platinum–iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material? `V=πr^2h`, `ρ=m/V`
Density: `ρ =2.15 times 10^4 kg//m^3`
Knowns:
`m=1 kg`
`h=39.0mm =3.90 times 10^(-2) m`
`d=39.0mm = 3.90 times 10^(-2) m`
Radius of the cylinder:
`r=d/2`
Volume of the cylinder:
`V=πr^2h =π(d/2)^2h`
Density of the cylinder:
`ρ=m/V`
`=m/(π(d/2)^2h)`
`=(1kg)/(π(3.90/2 times 10^(-2))^2(3.90 times 10^(-2)))`
`=2.15 times 10^4 kg//m^3`
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