# What is the density in g/cm^3 of an iron ball that has a radius of 45.0 mm, and a mass of 300 g?

Dec 4, 2017

The question states we have a "ball", or sphere, so we may calculate the volume,

$V = \frac{4 \pi {r}^{3}}{3}$

$V = \frac{4 \pi \cdot {\left(\left(45.0 m m\right) \cdot \frac{c m}{10 m m}\right)}^{3}}{3} \approx 382 c {m}^{3}$

From here, we may calculate density. Hence,

$\frac{300 g}{382 c {m}^{3}} \approx \frac{0.786 g}{c {m}^{3}}$

is the density of iron in this case, although this is a gross underestimation.