质量相等的实心铜球与实心的铝球的体积之比为_;体积相等的实心铜球和实心的铝球的质量之比为_.(ρ铜=8.9g/cm3,ρ铝=2.7g/cm3)

问题描述:

质量相等的实心铜球与实心的铝球的体积之比为______;体积相等的实心铜球和实心的铝球的质量之比为______.(ρ=8.9g/cm3,ρ=2.7g/cm3

由题知,ρ:ρ=8.9g/cm3:2.7g/cm3=89:27,
若铜和铝质量相等,即m:m=1:1,
∵ρ=

m
v

∴v=
m
ρ

∴v:v=
m
ρ
m
ρ
=
m
ρ
×
ρ
m
=
m
m
×
ρ
ρ
=
1
1
×
27
89
=27:89;
若铜和铝体积相等,即v:v=1:1,
∵ρ=
m
v

∴m=ρv,
∴m:m=
ρv
ρv
=
ρ
ρ
×
v
v
=
89
27
×
1
1
=89:27.
故答案为:27:89;89:27.