What Is The Volume Of A Rectangular Prism With A Height Of 9 M, A Length Of 5 M, And A Width Of 3 M?A. 180 M 3 180 \, \text{m}^3 180 M 3 B. 135 M 3 135 \, \text{m}^3 135 M 3 C. 108 M 3 108 \, \text{m}^3 108 M 3 D. 90 M 3 90 \, \text{m}^3 90 M 3
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Understanding the Concept of Volume
The volume of a rectangular prism is a fundamental concept in mathematics, particularly in geometry. It is defined as the amount of space inside the prism, measured in cubic units (e.g., cubic meters, cubic feet). The volume of a rectangular prism can be calculated using the formula: Volume = Length × Width × Height.
Given Dimensions of the Rectangular Prism
In this problem, we are given the dimensions of a rectangular prism as follows:
- Height (h): 9 meters
- Length (l): 5 meters
- Width (w): 3 meters
Calculating the Volume
To calculate the volume of the rectangular prism, we simply multiply the given dimensions together:
Volume = Length × Width × Height Volume = 5 m × 3 m × 9 m Volume = 135 m³
Conclusion
Therefore, the volume of the rectangular prism with a height of 9 m, a length of 5 m, and a width of 3 m is 135 m³.
Why is this Important?
Understanding the concept of volume is crucial in various real-world applications, such as:
- Architecture: Calculating the volume of a building or a room to determine the amount of materials needed for construction.
- Engineering: Calculating the volume of a container or a tank to determine the amount of liquid it can hold.
- Science: Calculating the volume of a sample or a container to determine the amount of substance it contains.
Common Mistakes to Avoid
When calculating the volume of a rectangular prism, it is essential to:
- Double-check the dimensions: Ensure that the given dimensions are correct and consistent.
- Use the correct formula: Use the formula Volume = Length × Width × Height to calculate the volume.
- Perform the calculation correctly: Multiply the dimensions together to get the correct volume.
Real-World Examples
Here are some real-world examples of calculating the volume of a rectangular prism:
- Building a house: A builder needs to calculate the volume of a room to determine the amount of materials needed for construction.
- Designing a container: An engineer needs to calculate the volume of a container to determine the amount of liquid it can hold.
- Measuring a sample: A scientist needs to calculate the volume of a sample to determine the amount of substance it contains.
Conclusion
In conclusion, calculating the volume of a rectangular prism is a fundamental concept in mathematics that has numerous real-world applications. By understanding the concept of volume and using the correct formula, we can calculate the volume of a rectangular prism with ease.
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Q: What is the formula for calculating the volume of a rectangular prism?
A: The formula for calculating the volume of a rectangular prism is: Volume = Length × Width × Height.
Q: What are the dimensions required to calculate the volume of a rectangular prism?
A: To calculate the volume of a rectangular prism, you need to know the following dimensions:
- Length (l): The length of the prism
- Width (w): The width of the prism
- Height (h): The height of the prism
Q: How do I calculate the volume of a rectangular prism with a height of 10 m, a length of 6 m, and a width of 4 m?
A: To calculate the volume of the rectangular prism, you can use the formula: Volume = Length × Width × Height.
Volume = 6 m × 4 m × 10 m Volume = 240 m³
Q: What is the volume of a rectangular prism with a height of 8 m, a length of 3 m, and a width of 2 m?
A: To calculate the volume of the rectangular prism, you can use the formula: Volume = Length × Width × Height.
Volume = 3 m × 2 m × 8 m Volume = 48 m³
Q: Can I calculate the volume of a rectangular prism with a height of 12 m, a length of 9 m, and a width of 6 m?
A: Yes, you can calculate the volume of the rectangular prism using the formula: Volume = Length × Width × Height.
Volume = 9 m × 6 m × 12 m Volume = 648 m³
Q: What is the volume of a rectangular prism with a height of 15 m, a length of 10 m, and a width of 8 m?
A: To calculate the volume of the rectangular prism, you can use the formula: Volume = Length × Width × Height.
Volume = 10 m × 8 m × 15 m Volume = 1200 m³
Q: Can I calculate the volume of a rectangular prism with a height of 20 m, a length of 12 m, and a width of 10 m?
A: Yes, you can calculate the volume of the rectangular prism using the formula: Volume = Length × Width × Height.
Volume = 12 m × 10 m × 20 m Volume = 2400 m³
Q: What is the volume of a rectangular prism with a height of 25 m, a length of 15 m, and a width of 12 m?
A: To calculate the volume of the rectangular prism, you can use the formula: Volume = Length × Width × Height.
Volume = 15 m × 12 m × 25 m Volume = 4500 m³
Conclusion
In conclusion, calculating the volume of a rectangular prism is a fundamental concept in mathematics that has numerous real-world applications. By understanding the concept of volume and using the correct formula, we can calculate the volume of a rectangular prism with ease.