Question

A small cube-shaped particle of iron is observed under a microscope. The edge of the cube is 12 micrometers, and the density of the iron is 7.8 g/cm³. Find the mass.

Answer 1

To find the mass of the iron cube, first convert the edge length to centimeters, calculate the volume of the cube, and then multiply by the density of iron (7.8 g/cm³) to get the mass.

Step-by-step explanation:

The student is asking to calculate the mass of a small cube-shaped particle of iron with given dimensions and density. To find the mass, we need to first calculate the volume of the iron cube and then use the density to find the mass.

Step-by-step explanation:

1. Convert the edge length from micrometers to centimeters: 12 micrometers = 0.0012 centimeters.
2. Calculate the volume of the cube (V) using the formula V = edge length3: V = 0.0012 cm x 0.0012 cm x 0.0012 cm = 1.728 x 10-9 cm3.
3. Use the density (ρ) of iron, 7.8 g/cm3, to find the mass (m) using the formula m = ρ x V: m = 7.8 g/cm3 x 1.728 x 10-9 cm3.
4. Calculate the mass: m = 1.348 x 10-8 grams.