1 Answer

Luisenrique · Answer 1 · 2022-06-06T14:19:05+0000

Answer:

The radius of the ball is 3.48 cm

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:

$\displaystyle \rho=(m)/(V)$

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:

$\displaystyle V=(m)/(\rho)$

$\displaystyle V=(2000\ g)/(11.35\ g/cm^3)$

$V=176.2115\ cm^3$

Since the shape of the object is a sphere, and the volume of a sphere of radius r is:

$\displaystyle V=(4)/(3)\cdot \pi\cdot r^3$

We can solve for r and obtain:

$\displaystyle r=\sqrt[3]{(3V)/(4\pi)}$

Substituting:

$\displaystyle r=\sqrt[3]{(3*176.2115)/(4\pi)}$

$\displaystyle r=\sqrt[3]{42.0674}$

$\boxed{r=3.48\ cm}$

The radius of the ball is 3.48 cm

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