Answer:
<em>The mass of the steel ball is 4,235.9 gr</em>
Step-by-step explanation:
<u>Density</u>
The density ρ of a substance is a measure of its mass per unit volume:
![\displaystyle \rho=\frac{m}{V}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Crho%3D%5Cfrac%7Bm%7D%7BV%7D)
If the density and the volume are given, the mass can be calculated by solving the above formula for m:
![m=\rho.V](https://tex.z-dn.net/?f=m%3D%5Crho.V)
We know the density of pure steel ρ=8.09 gr/cm3 and the diameter of a solid steel ball d=10 cm.
We need to calculate the volume of the sphere:
The volume of a sphere of radius r is given by:
![\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cfrac%7B4%7D%7B3%7D%5Ccdot%20%5Cpi%5Ccdot%20r%5E3)
The radius is half the diameter: r= 10/2 = 5 cm. Thus:
![\displaystyle V=\frac{4}{3}\cdot \pi\cdot 5^3](https://tex.z-dn.net/?f=%5Cdisplaystyle%20V%3D%5Cfrac%7B4%7D%7B3%7D%5Ccdot%20%5Cpi%5Ccdot%205%5E3)
Calculating:
![V=523.6\ cm^3](https://tex.z-dn.net/?f=V%3D523.6%5C%20cm%5E3)
The mass is:
![m=8.09 gr/cm^3 \cdot 523.6\ cm^3](https://tex.z-dn.net/?f=m%3D8.09%20gr%2Fcm%5E3%20%5Ccdot%20523.6%5C%20cm%5E3)
m=4,235.9 gr
The mass of the steel ball is 4,235.9 gr