What Is The Volume Of A Right Rectangular Prism With A Height Of 12 Feet And A Base That Is A Rectangle Measuring 4 Feet By 7 Feet?A. $48 \, \text{ft}^3$ B. $84 \, \text{ft}^3$ C. $132 \, \text{ft}^3$ D. $336 \,
Introduction
In geometry, a right rectangular prism is a three-dimensional shape with six rectangular faces, where all angles are right angles. The volume of a right rectangular prism is a crucial concept in mathematics, as it helps us calculate the amount of space inside the prism. In this article, we will explore the concept of the volume of a right rectangular prism and provide a step-by-step solution to find the volume of a specific prism.
What is the Volume of a Right Rectangular Prism?
The volume of a right rectangular prism is calculated by multiplying the length, width, and height of the prism. The formula for the volume of a right rectangular prism is:
V = lwh
Where:
- V is the volume of the prism
- l is the length of the prism
- w is the width of the prism
- h is the height of the prism
Calculating the Volume of a Right Rectangular Prism
To calculate the volume of a right rectangular prism, we need to know the length, width, and height of the prism. Let's consider a specific prism with a height of 12 feet and a base that is a rectangle measuring 4 feet by 7 feet.
Given Information
- Height (h) = 12 feet
- Length (l) = 4 feet
- Width (w) = 7 feet
Step 1: Identify the Given Information
We have been given the height, length, and width of the prism. We can use this information to calculate the volume of the prism.
Step 2: Plug in the Values into the Formula
Now that we have the given information, we can plug in the values into the formula:
V = lwh V = (4)(7)(12)
Step 3: Calculate the Volume
To calculate the volume, we need to multiply the length, width, and height of the prism:
V = (4)(7)(12) V = 28(12) V = 336
Conclusion
The volume of a right rectangular prism is calculated by multiplying the length, width, and height of the prism. In this article, we have provided a step-by-step solution to find the volume of a specific prism with a height of 12 feet and a base that is a rectangle measuring 4 feet by 7 feet. The volume of the prism is 336 cubic feet.
Answer
The correct answer is:
- D. 336
Why is this Important?
Understanding the volume of a right rectangular prism is crucial in various fields, such as architecture, engineering, and design. It helps us calculate the amount of space inside a three-dimensional shape, which is essential in designing buildings, bridges, and other structures.
Real-World Applications
The concept of the volume of a right rectangular prism has numerous real-world applications, such as:
- Architecture: Architects use the volume of a right rectangular prism to calculate the amount of space inside a building.
- Engineering: Engineers use the volume of a right rectangular prism to calculate the amount of material needed for a project.
- Design: Designers use the volume of a right rectangular prism to calculate the amount of space inside a product.
Conclusion
Q: What is the formula for the volume of a right rectangular prism?
A: The formula for the volume of a right rectangular prism is V = lwh, where V is the volume, l is the length, w is the width, and h is the height.
Q: How do I calculate the volume of a right rectangular prism?
A: To calculate the volume of a right rectangular prism, you need to multiply the length, width, and height of the prism. For example, if the length is 4 feet, the width is 7 feet, and the height is 12 feet, the volume would be V = (4)(7)(12) = 336 cubic feet.
Q: What if the prism has a different shape, such as a triangle or a circle?
A: The formula V = lwh only applies to right rectangular prisms. If the prism has a different shape, you would need to use a different formula to calculate its volume.
Q: Can I use the volume of a right rectangular prism to calculate the volume of a different shape?
A: No, the volume of a right rectangular prism is specific to that shape and cannot be used to calculate the volume of a different shape.
Q: How do I apply the concept of volume to real-world problems?
A: The concept of volume can be applied to various real-world problems, such as:
- Calculating the amount of space inside a building or a room
- Determining the amount of material needed for a construction project
- Designing products with specific volume requirements
Q: What are some common mistakes to avoid when calculating the volume of a right rectangular prism?
A: Some common mistakes to avoid when calculating the volume of a right rectangular prism include:
- Forgetting to multiply the length, width, and height
- Using the wrong units (e.g., feet instead of inches)
- Not considering the shape of the prism (e.g., using the formula for a right rectangular prism for a different shape)
Q: How can I practice calculating the volume of a right rectangular prism?
A: You can practice calculating the volume of a right rectangular prism by:
- Using online calculators or worksheets
- Creating your own problems and solutions
- Working with real-world examples, such as calculating the volume of a room or a box
Q: What are some advanced concepts related to the volume of a right rectangular prism?
A: Some advanced concepts related to the volume of a right rectangular prism include:
- Calculating the volume of irregular shapes
- Using calculus to find the volume of a shape
- Applying the concept of volume to three-dimensional geometry
Conclusion
In conclusion, the volume of a right rectangular prism is a fundamental concept in mathematics that has numerous real-world applications. By understanding the formula and applying it to various problems, you can develop a deeper understanding of the concept and improve your problem-solving skills.