A rectangular object has the following dimensions: length 2.00 cm, height 3.00 cm and the width 1.50 cm. It weight is 34.26 grams. What is the density of the object?
The Correct Answer and Explanation is:
To calculate the density of the rectangular object, we can use the formula:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}}
]
Step 1: Calculate the Volume
The volume of a rectangular object is given by the formula:
[
\text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
]
Given the dimensions:
- Length = 2.00 cm
- Width = 1.50 cm
- Height = 3.00 cm
Now, plug in the values:
[
\text{Volume} = 2.00 \, \text{cm} \times 1.50 \, \text{cm} \times 3.00 \, \text{cm}
]
[
\text{Volume} = 9.00 \, \text{cm}^3
]
Step 2: Use the Formula for Density
The mass of the object is given as 34.26 grams.
Now, we can calculate the density using the formula:
[
\text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{34.26 \, \text{g}}{9.00 \, \text{cm}^3}
]
[
\text{Density} = 3.81 \, \text{g/cm}^3
]
Explanation
Density is a property of matter that describes how much mass is packed into a given volume. It is an important physical property because it helps us identify materials and predict their behavior when placed in different environments, such as whether an object will float or sink in a fluid. The density of an object depends on both its mass (how much matter it contains) and its volume (how much space it occupies).
In this case, we have a rectangular object with a mass of 34.26 grams and dimensions of 2.00 cm by 1.50 cm by 3.00 cm. By calculating the volume using the formula for the volume of a rectangle and dividing the mass by this volume, we find that the density is 3.81 g/cm³. This means that for every cubic centimeter of this material, there is 3.81 grams of mass.
Density is often used in material science, engineering, and physics to describe the characteristics of different substances. If the object is made of a known material, its density can be compared to the typical density values of substances to help identify it.