Answer
The diameter of the sphere is 8.4 cm
Work Step by Step
We can find the mass of the aluminum as:
$m = \rho~V$
$m = (2.70\times 10^3~kg/m^3)(1000~cm^3)$
$m = (2.70\times 10^3~kg/m^3)(1000\times 10^{-6}~m^3)$
$m = 2.70~kg$
We can find the volume of copper that has this mass as:
$V = \frac{m}{\rho}$
$V = \frac{2.70~kg}{8.9\times 10^3~kg/m^3}$
$V = 3.034\times 10^{-4}~m^3$
We can find the radius of the copper sphere as:
$\frac{4}{3}\pi~R^3 = V$
$R^3 = \frac{3V}{4\pi}$
$R = (\frac{3V}{4\pi})^{(1/3)}$
$R = [\frac{(3)(3.034\times 10^{-4}~m^3)}{4\pi}]^{(1/3)}$
$R = 0.042~m = 4.2~cm$
Since the diameter of the sphere is $2R$, the diameter of the sphere is 8.4 cm.
