Answer:
1.33 cm
Explanation:
Mass of copper, [tex]m=243 g[/tex]
Side of the cube, [tex]a=3 cm[/tex]
Volume of the copper cube, [tex]a^3=(3cm)^3=27cm^3[/tex]
Density of copper, [tex]density =\frac{mass}{volume}[/tex]
[tex]\rho=\frac{243gm}{27cm^3}=9gm/cm^3[/tex]
Let the radius of the sphere be r.
Volume of the copper sphere, [tex]V=\frac{4}{3}\pi r^3[/tex]
[tex]V=\frac{m}{\rho}\\\Rightarrow \frac{4}{3}\pi r^3= \frac{m}{\rho}\\\Rightarrow r =\sqrt[3]{ {\frac{3m}{4\pi \rho}}}[/tex]
If the mass is 50 g, then the radius of the copper sphere is:
[tex]r=\sqrt[3]{\frac{3\times 50g}{4\pi 9g/cm^3}} =1.33 cm[/tex]
