Question

Determine the mass of a solid steel ball that has a diameter of 10 cm. The density of pure steel is 8.09 g/cm3

Answer 1

Answer:

The mass of the steel ball is 4,235.9 gr

Step-by-step explanation:

Density

The density ρ of a substance is a measure of its mass per unit volume:

$\displaystyle \rho=\frac{m}{V}$

If the density and the volume are given, the mass can be calculated by solving the above formula for m:

$m=\rho.V$

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:

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

The radius is half the diameter: r= 10/2 = 5 cm. Thus:

$\displaystyle V=\frac{4}{3}\cdot \pi\cdot 5^3$

Calculating:

$V=523.6\ cm^3$

The mass is:

$m=8.09 gr/cm^3 \cdot 523.6\ cm^3$

m=4,235.9 gr

The mass of the steel ball is 4,235.9 gr