# How Many Cobalt Atoms Are There in an Alloy Cylinder?

How many cobalt atoms are there in a cylinder of radius 2.5cm and a length of 10 cm?

The number of cobalt atoms in a cylinder of the alloy with a radius of 2.5cm and height of 10cm is approximately 1.98 × 10²⁴.

## Calculation of Cobalt Atoms in Alloy Cylinder

**To calculate the number of cobalt atoms in the said alloy cylinder, we first need to figure out the volume of the cylinder. Using the cylinder volume formula (πr²h), where r=2.5cm and h=10cm, the volume is approximately 196.3cm³. However, the density of the alloy is given in grams/ml, and since 1 ml equals 1 cm³, the mass of the alloy can be calculated as 8.2g/ml * 196.3ml = 1609.66g. Next, considering that cobalt constitutes 12% of the alloy, the mass of cobalt in the alloy is 12/100 * 1609.66g = 193.16g. We then convert this mass into moles using the atomic mass of cobalt (58.9g/mol), hence, the moles of cobalt are 193.16g / 58.9g/mol = 3.28 mol. Finally, by using Avogadro's number (6.022 × 10²³ atoms/mol), we can calculate the number of atoms. The number of cobalt atoms in the alloy cylinder is 3.28 mol * 6.022 × 10²³ atoms/mol ≈ 1.98 × 10²⁴ atoms.**