Answer:
[tex]\frac{r_{Al}}{r_{Zn} }= 1.625 : 1[/tex]
Explanation:
[tex]density = \frac{mass}{volume} [/tex]
ρ =[tex] \frac{m}{v}[/tex]
making mass subject of formula we have
m=ρv
from the question aluminium and zinc have same mass hence we can say;
[tex]m_{Al}=m_{Zn}[/tex]
which means; [tex]ρ_{Al} V_{Al}=ρ_{Zn} V_{Zn}[/tex]
[tex]\frac{ρ_{Al} }{ρ_{Zn} }= =\frac{V_{Zn} }{V_{Al} }[/tex]
[tex] \frac{ρ_{Al} }{ρ_{Zn} }= =\frac{4\pi r_{Zn} ^{3} }{4\pi r_{Al}^{3} }[/tex]
[tex]\frac{ρ_{Al} }{ρ_{Zn} }= =\frac{r_{Zn} ^{3} }{r_{Al}^{3} } [/tex]
[tex]\frac{ρ_{Al} }{ρ_{Zn} }= =(\frac{r_{Zn}}{r_{Al} })^{3} [/tex]
[tex]\frac{r_{Zn}}{r_{Al} }= \sqrt{\frac{ρ_{Al} }{ρ_{Zn} }}[/tex]
[tex]{ρ_{Al}= 2700{/tex]
[tex]{ρ_{Zn}= 7130{/tex]
[tex]\frac{r_{Zn}}{r_{Al} }=\sqrt{\frac{2700 }{7130} }}[/tex]
[tex]\frac{r_{Zn}}{r_{Al} }= 0.6154[/tex]
[tex]\frac{r_{Al}}{r_{Zn} }=\frac{1}{0.6154}[/tex]
[tex]\frac{r_{Al}}{r_{Zn} }= 1.625 : 1[/tex]
