Answer:
The radius of the ball is 3.48 cm
Step-by-step explanation:
Density
The density of a substance is the mass per unit volume. The density varies with temperature and pressure.
The formula to calculate the density of a substance of mass (m) and volume (V) is:
[tex]\displaystyle \rho=\frac{m}{V}[/tex]
The density of lead is \rho=11.35\ g/cm^3 and the mass of a ball of lead is m=2 kg=2,000 g. We can calculate the volume by solving for V:
[tex]\displaystyle V=\frac{m}{\rho}[/tex]
[tex]\displaystyle V=\frac{2000\ g}{11.35\ g/cm^3}[/tex]
[tex]V=176.2115\ cm^3[/tex]
Since the shape of the object is a sphere, and the volume of a sphere of radius r is:
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3[/tex]
We can solve for r and obtain:
[tex]\displaystyle r=\sqrt[3]{\frac{3V}{4\pi}}[/tex]
Substituting:
[tex]\displaystyle r=\sqrt[3]{\frac{3*176.2115}{4\pi}}[/tex]
[tex]\displaystyle r=\sqrt[3]{42.0674}[/tex]
[tex]\boxed{r=3.48\ cm}[/tex]
The radius of the ball is 3.48 cm
