What is the mass of a magnesium block that measures 2.00 cm × 6.00 cm × 5.00 cm? The density of magnesium is 1.738 g/cm3.
The Correct Answer and Explanation is :
To calculate the mass of a magnesium block, you can use the formula:
[
\text{Mass} = \text{Density} \times \text{Volume}
]
Step 1: Calculate the Volume
First, calculate the volume of the magnesium block using its dimensions. The formula for the volume ( V ) of a rectangular block is:
[
V = \text{length} \times \text{width} \times \text{height}
]
Given the dimensions of the magnesium block:
- Length = 2.00 cm
- Width = 6.00 cm
- Height = 5.00 cm
Substituting the values:
[
V = 2.00 \, \text{cm} \times 6.00 \, \text{cm} \times 5.00 \, \text{cm} = 60.00 \, \text{cm}^3
]
Step 2: Use the Density to Find the Mass
Now, you can find the mass using the density of magnesium, which is given as 1.738 g/cm³.
Substituting the values into the mass formula:
[
\text{Mass} = \text{Density} \times \text{Volume}
]
[
\text{Mass} = 1.738 \, \text{g/cm}^3 \times 60.00 \, \text{cm}^3
]
[
\text{Mass} = 104.28 \, \text{g}
]
Conclusion
Thus, the mass of the magnesium block is approximately 104.28 grams.
Explanation
In this calculation, the volume is determined by multiplying the block’s length, width, and height, which gives a total volume of 60 cm³. The density of magnesium, which is the mass per unit volume, is then applied to find the total mass of the block. The density provides a measure of how much mass is contained within a specific volume of the material. Magnesium is a lightweight metal, which is why the mass calculated here is relatively low, despite the block’s sizable dimensions. Understanding the relationship between volume, mass, and density is fundamental in material science and engineering, allowing for precise calculations and applications in various fields, including manufacturing and construction.