The mass of the rectangular prism below is 10 g. What is the density of the rectangular prism below? 3 cm 2 cm 4 cm
The Correct Answer and Explanation is:
To determine the density of the rectangular prism, we use the formula:
Density=MassVolume\text{Density} = \frac{\text{Mass}}{\text{Volume}}
First, we calculate the volume of the prism. The volume of a rectangular prism is given by:
V=length×width×heightV = \text{length} \times \text{width} \times \text{height}
Substituting the given values:
V=4 cm×2 cm×3 cm=24 cm3V = 4 \text{ cm} \times 2 \text{ cm} \times 3 \text{ cm} = 24 \text{ cm}^3
Now, using the provided mass of 10 grams:
Density=10 g24 cm3\text{Density} = \frac{10 \text{ g}}{24 \text{ cm}^3}
Performing the division:
Density=0.4167 g/cm3\text{Density} = 0.4167 \text{ g/cm}^3
The density of the rectangular prism is approximately 0.4167 grams per cubic centimeter.
Explanation
Density is a measure of how much mass is contained within a given volume. It represents how compact or spread out the material is. The formula for density is mass divided by volume, which provides a ratio of mass per unit of space occupied.
In this case, we first determined the volume of the prism by multiplying its length, width, and height. This calculation gives the total space the object occupies. Once we have the volume, we use the provided mass to compute density by dividing mass by volume.
Density is a fundamental concept in physics and material science. It helps in identifying substances, understanding buoyancy, and optimizing material usage in engineering. Objects with higher density tend to sink in fluids, while those with lower density may float. For instance, comparing metals and wood, metals typically have greater density, making them heavier for the same volume.
This concept is widely used in real-world applications, including designing materials for construction, selecting suitable materials for packaging, and analyzing the properties of fluids. Understanding density aids in various practical scenarios, such as predicting whether an object will sink or float in water or ensuring efficient material utilization in industrial processes.
