The density of the spherical ball can be calculated using the formula:

Density = Mass/Volume

Given that the ball contains 66.66% by mass iron, the remaining mass must be due to the other elements present in the ball. Let's assume that the ball is made up of only iron and some other element (let's call it X).

Therefore, the mass of iron in the ball can be calculated as:

Mass of Iron = 0.6666 * Total Mass of the Ball

Similarly, the mass of element X can be calculated as:

Mass of X = 0.3334 * Total Mass of the Ball

Now, we can calculate the density of the ball using the above values and the radius of the ball:

Density = (Mass of Iron + Mass of X)/(4/3 * π * (3 cm)^3)


Once we have calculated the density of the ball, we can use the formula for density to calculate the number of moles of iron present in the ball:

Density = Mass/Volume

Mass = Density * Volume

Volume of the ball = 4/3 * π * (3 cm)^3

Now, we can calculate the mass of iron in the ball using the density value we calculated earlier:

Mass of Iron = Density * Volume * 0.6666

Finally, we can calculate the number of moles of iron using the following formula:

Number of Moles of Iron = Mass of Iron/Molar Mass of Iron

The molar mass of iron is 55.845 g/mol.

Therefore, the number of moles of iron in the spherical ball can be calculated using the above formula.

0.04 mol