Answer :
- Use the formula:$\text{Density} = \frac{\text{Mass}}{\text{Volume}}$
- Rearrange the formula to solve for volume: $\text{Volume} = \frac{\text{Mass}}{\text{Density}}$
- Substitute the given values: $\text{Volume} = \frac{98.1}{2.18}$
- Calculate the volume and round to the tenths place: $\boxed{45.0 \text{ cm}^3}$
### Explanation
1. Understanding the Problem
We are given the mass and density of a piece of asphalt and asked to calculate its volume. We know that density is defined as mass per unit volume, which gives us the formula:$$Density = \frac{Mass}{Volume}$$
2. Rearranging the Formula
To find the volume, we need to rearrange the formula to solve for volume:$$Volume = \frac{Mass}{Density}$$
3. Substituting the Values
Now, we can substitute the given values into the formula. The mass of the asphalt is 98.1 grams, and its density is 2.18 grams per cubic centimeter. Therefore,$$Volume = \frac{98.1 \text{ grams}}{2.18 \text{ grams/cm}^3}$$
4. Calculating the Volume and Rounding
Performing the division, we find:$$Volume = 44.99 \approx 45.0 \text{ cm}^3$$We are asked to round the answer to the tenths place, so the volume is approximately 45.0 cubic centimeters.
5. Final Answer
Therefore, the volume of the piece of asphalt is approximately 45.0 cubic centimeters.
### Examples
Understanding density and volume calculations is crucial in many real-world applications, such as determining the composition of materials, designing structures, and calculating buoyancy. For example, engineers use these principles to ensure bridges can withstand specific loads, and marine biologists use them to study the properties of ocean water. Knowing how to calculate volume from mass and density helps in various fields, from construction to environmental science, making it a valuable skill.
- Rearrange the formula to solve for volume: $\text{Volume} = \frac{\text{Mass}}{\text{Density}}$
- Substitute the given values: $\text{Volume} = \frac{98.1}{2.18}$
- Calculate the volume and round to the tenths place: $\boxed{45.0 \text{ cm}^3}$
### Explanation
1. Understanding the Problem
We are given the mass and density of a piece of asphalt and asked to calculate its volume. We know that density is defined as mass per unit volume, which gives us the formula:$$Density = \frac{Mass}{Volume}$$
2. Rearranging the Formula
To find the volume, we need to rearrange the formula to solve for volume:$$Volume = \frac{Mass}{Density}$$
3. Substituting the Values
Now, we can substitute the given values into the formula. The mass of the asphalt is 98.1 grams, and its density is 2.18 grams per cubic centimeter. Therefore,$$Volume = \frac{98.1 \text{ grams}}{2.18 \text{ grams/cm}^3}$$
4. Calculating the Volume and Rounding
Performing the division, we find:$$Volume = 44.99 \approx 45.0 \text{ cm}^3$$We are asked to round the answer to the tenths place, so the volume is approximately 45.0 cubic centimeters.
5. Final Answer
Therefore, the volume of the piece of asphalt is approximately 45.0 cubic centimeters.
### Examples
Understanding density and volume calculations is crucial in many real-world applications, such as determining the composition of materials, designing structures, and calculating buoyancy. For example, engineers use these principles to ensure bridges can withstand specific loads, and marine biologists use them to study the properties of ocean water. Knowing how to calculate volume from mass and density helps in various fields, from construction to environmental science, making it a valuable skill.
