A cubic piece of metal measures 5.00 cm on each edge. If the metal is nickel, whose density is 8.90 g/cm³, what is the mass of the cube?
The Correct Answer and Explanation is:
To calculate the mass of the cubic piece of metal, we can use the formula for density:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Rearranging this equation to solve for mass:
[
\text{Mass} = \text{Density} \times \text{Volume}
]
Step 1: Find the volume of the cube
The volume of a cube is calculated using the formula:
[
\text{Volume} = \text{side}^3
]
Since each edge of the cube is 5.00 cm, the volume is:
[
\text{Volume} = (5.00 \, \text{cm})^3 = 5.00 \times 5.00 \times 5.00 = 125.00 \, \text{cm}^3
]
Step 2: Apply the density to find the mass
The density of nickel is given as 8.90 g/cm³. Now, we can substitute the values for density and volume into the formula for mass:
[
\text{Mass} = 8.90 \, \text{g/cm}^3 \times 125.00 \, \text{cm}^3 = 1112.50 \, \text{g}
]
Thus, the mass of the cube is 1112.50 grams.
Explanation:
Density is defined as the mass of an object per unit volume. For the nickel cube, we are given its density and the dimensions of the cube (which are 5.00 cm for each edge). The formula for volume of a cube involves cubing the length of one edge. Once the volume is calculated, the mass can be determined by multiplying the volume by the given density.
In this case, since nickel has a relatively high density (8.90 g/cm³), a cube with a volume of 125 cm³ results in a substantial mass. By using the relationship between mass, volume, and density, we find that the mass of the cube is 1112.50 grams, or about 1.11 kilograms. This shows how density can be used to determine mass, provided both the material’s density and the object’s volume are known.