Solution :

Let $l=l_{Al}$ density $d_{Al}=2.7$

and area $A{Al}=A_1$ and

For copper

Let $l= l_{cn}$

Density $d_{cn} =8.9$

and $ A_{cn} =A_2$

Also $l_{Al}= l_{cn}=l$

$R= \rho \large\frac{l}{A}$

Resistance for aluminium wire $R_{Al} =\rho_{Al} \times \large\frac{l_{Al}}{A_{Al}}$

mass of the aluminium wire

$m_{Al} =A{Al} \times l_{Al} \times d_{Al}$

$\quad= A_1 \times l \times 2.7$

Resistance of the copper wire ,

$R_{cn}=\rho_{cn} $$\times \large\frac{l_{cn}}{A_{cn}}$

$\qquad= \large\frac{1.72 \times 10^{-8} \times l}{A_2}$

mass of copper wire $m_{cn} =A_{cn} \times l_{cn} \times d_{cn}$

$\qquad= A_2 \times l \times 8.9$

But it is given that $R_{Al} =R_{cn}$

$\therefore \large\frac{2.63 \times 10^{-8} \times l}{A_2}$

$\large\frac{A_1}{A_2}=\frac{2.63}{1.72}$

$\large\frac{m_{Al}}{m_{cn}}=\frac{ A_1 \times l \times 2.7}{A_2 \times l \times 8.9}$

$\large\frac{m_{Al}}{m_{cn}}=\frac{ 2.63 \times 2.7}{1.72 \times 89}$

$\qquad= 2.16$

Hence copper wires are $2.16$ times heavier than aluminium .

Answer : Copper wires are 2.16 times heavier than aluminium