Kaylee Found The Surface Area, In Square Inches, Of A Rectangular Prism By Using This Formula:$\[ 2(5 \times 3) + 2(5 \times 8) + 2(3 \times 8) \\]What Is The Surface Area Of The Prism, In Square Inches?A. 158 B. 85 C. 40 D. 238
Introduction
In mathematics, the surface area of a rectangular prism is a crucial concept that helps us calculate the total area of its external surface. It is an essential aspect of geometry and is used in various real-world applications, such as architecture, engineering, and design. In this article, we will delve into the formula for calculating the surface area of a rectangular prism and provide a step-by-step solution to a problem presented by Kaylee.
The Formula for Surface Area
The surface area of a rectangular prism can be calculated using the following formula:
where:
- is the length of the prism
- is the width of the prism
- is the height of the prism
This formula calculates the total surface area by adding the areas of all six faces of the prism.
Breaking Down the Formula
Let's break down the formula into its individual components:
- represents the area of the two faces with dimensions and
- represents the area of the two faces with dimensions and
- represents the area of the two faces with dimensions and
Applying the Formula to Kaylee's Problem
Kaylee used the following formula to calculate the surface area of a rectangular prism:
To solve this problem, we need to follow the order of operations (PEMDAS):
- Multiply the numbers inside the parentheses:
- Multiply the results by 2:
- Add the results together:
Therefore, the surface area of the prism is 158 square inches.
Conclusion
In conclusion, the surface area of a rectangular prism can be calculated using the formula . By breaking down the formula into its individual components and following the order of operations, we can solve problems like Kaylee's and find the surface area of a rectangular prism.
Real-World Applications
The surface area of a rectangular prism has numerous real-world applications, such as:
- Architecture: Architects use the surface area of a building to determine the amount of materials needed for construction.
- Engineering: Engineers use the surface area of a machine or device to determine its efficiency and performance.
- Design: Designers use the surface area of a product to determine its aesthetic appeal and functionality.
Common Mistakes
When calculating the surface area of a rectangular prism, it's essential to avoid common mistakes, such as:
- Incorrect dimensions: Make sure to use the correct dimensions of the prism.
- Incorrect formula: Use the correct formula for calculating the surface area.
- Incorrect order of operations: Follow the order of operations (PEMDAS) to ensure accurate results.
Practice Problems
To practice calculating the surface area of a rectangular prism, try the following problems:
- A rectangular prism has dimensions of 6 inches, 8 inches, and 10 inches. What is its surface area?
- A rectangular prism has dimensions of 4 inches, 6 inches, and 8 inches. What is its surface area?
Answer Key
- A rectangular prism with dimensions of 6 inches, 8 inches, and 10 inches has a surface area of 2(6 \times 8) + 2(6 \times 10) + 2(8 \times 10) = 2(48) + 2(60) + 2(80) = 96 + 120 + 160 = 376 square inches.
- A rectangular prism with dimensions of 4 inches, 6 inches, and 8 inches has a surface area of 2(4 \times 6) + 2(4 \times 8) + 2(6 \times 8) = 2(24) + 2(32) + 2(48) = 48 + 64 + 96 = 208 square inches.
Q: What is the surface area of a rectangular prism?
A: The surface area of a rectangular prism is the total area of its external surface. It is calculated using the formula: 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height of the prism, respectively.
Q: How do I calculate the surface area of a rectangular prism?
A: To calculate the surface area of a rectangular prism, follow these steps:
- Multiply the length and width to get the area of the two faces with dimensions l and w.
- Multiply the length and height to get the area of the two faces with dimensions l and h.
- Multiply the width and height to get the area of the two faces with dimensions w and h.
- Add the results together to get the total surface area.
Q: What are the dimensions of a rectangular prism?
A: The dimensions of a rectangular prism are its length (l), width (w), and height (h). These dimensions are used to calculate the surface area of the prism.
Q: How do I apply the formula for surface area to a problem?
A: To apply the formula for surface area to a problem, follow these steps:
- Identify the dimensions of the rectangular prism (l, w, and h).
- Plug the dimensions into the formula: 2lw + 2lh + 2wh.
- Multiply the numbers inside the parentheses.
- Multiply the results by 2.
- Add the results together to get the total surface area.
Q: What are some real-world applications of surface area of rectangular prisms?
A: The surface area of a rectangular prism has numerous real-world applications, such as:
- Architecture: Architects use the surface area of a building to determine the amount of materials needed for construction.
- Engineering: Engineers use the surface area of a machine or device to determine its efficiency and performance.
- Design: Designers use the surface area of a product to determine its aesthetic appeal and functionality.
Q: What are some common mistakes to avoid when calculating surface area?
A: Some common mistakes to avoid when calculating surface area include:
- Incorrect dimensions: Make sure to use the correct dimensions of the prism.
- Incorrect formula: Use the correct formula for calculating the surface area.
- Incorrect order of operations: Follow the order of operations (PEMDAS) to ensure accurate results.
Q: How do I practice calculating surface area of rectangular prisms?
A: To practice calculating surface area of rectangular prisms, try the following problems:
- A rectangular prism has dimensions of 6 inches, 8 inches, and 10 inches. What is its surface area?
- A rectangular prism has dimensions of 4 inches, 6 inches, and 8 inches. What is its surface area?
Q: What are some tips for calculating surface area of rectangular prisms?
A: Some tips for calculating surface area of rectangular prisms include:
- Use the correct formula: Make sure to use the correct formula for calculating the surface area.
- Follow the order of operations: Follow the order of operations (PEMDAS) to ensure accurate results.
- Check your work: Double-check your calculations to ensure accuracy.
By following these tips and practicing with problems, you can become proficient in calculating the surface area of rectangular prisms.