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. 40 B. 85 C. 238 D. 158

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Understanding the Formula

In mathematics, the surface area of a rectangular prism can be calculated using a specific formula. This formula takes into account the dimensions of the prism, which include the length, width, and height. The formula provided by Kaylee is: 2(5×3)+2(5×8)+2(3×8)2(5 \times 3) + 2(5 \times 8) + 2(3 \times 8).

Breaking Down the Formula

To calculate the surface area of the prism, we need to break down the formula into its individual components. The formula consists of three main parts:

  • 2(5×3)2(5 \times 3)
  • 2(5×8)2(5 \times 8)
  • 2(3×8)2(3 \times 8)

Calculating Each Component

Let's calculate each component of the formula:

  • 2(5×3)2(5 \times 3): This component involves multiplying the length and width of the prism, which are 5 and 3, respectively. The result is 2×15=302 \times 15 = 30.
  • 2(5×8)2(5 \times 8): This component involves multiplying the length and height of the prism, which are 5 and 8, respectively. The result is 2×40=802 \times 40 = 80.
  • 2(3×8)2(3 \times 8): This component involves multiplying the width and height of the prism, which are 3 and 8, respectively. The result is 2×24=482 \times 24 = 48.

Adding the Components

Now that we have calculated each component, we can add them together to find the total surface area of the prism:

30+80+48=15830 + 80 + 48 = 158

Conclusion

Therefore, the surface area of the prism, in square inches, is 158.

Why is this the Correct Answer?

The correct answer is 158 because it is the sum of the individual components of the formula. The formula provided by Kaylee is a valid method for calculating the surface area of a rectangular prism, and the result of 158 is the correct answer.

What is the Importance of Calculating Surface Area?

Calculating the surface area of a rectangular prism is an important concept in mathematics and has various real-world applications. For example, in architecture, engineers need to calculate the surface area of buildings to determine the amount of materials required for construction. In manufacturing, companies need to calculate the surface area of products to determine the amount of packaging materials required.

Real-World Applications of Surface Area

Surface area has various real-world applications, including:

  • Architecture: Engineers need to calculate the surface area of buildings to determine the amount of materials required for construction.
  • Manufacturing: Companies need to calculate the surface area of products to determine the amount of packaging materials required.
  • Packaging: Companies need to calculate the surface area of products to determine the amount of packaging materials required.
  • Design: Designers need to calculate the surface area of products to determine the amount of materials required for production.

Conclusion

Q: What is the formula for calculating the surface area of a rectangular prism?

A: The formula for calculating the surface area of a rectangular prism is: 2(5×3)+2(5×8)+2(3×8)2(5 \times 3) + 2(5 \times 8) + 2(3 \times 8).

Q: What are the individual components of the formula?

A: The individual components of the formula are:

  • 2(5×3)2(5 \times 3)
  • 2(5×8)2(5 \times 8)
  • 2(3×8)2(3 \times 8)

Q: How do I calculate each component of the formula?

A: To calculate each component of the formula, you need to multiply the dimensions of the prism and then multiply the result by 2.

  • For the first component, multiply the length and width of the prism (5 and 3, respectively) to get 15. Then, multiply 15 by 2 to get 30.
  • For the second component, multiply the length and height of the prism (5 and 8, respectively) to get 40. Then, multiply 40 by 2 to get 80.
  • For the third component, multiply the width and height of the prism (3 and 8, respectively) to get 24. Then, multiply 24 by 2 to get 48.

Q: How do I add the components together to find the total surface area?

A: To add the components together, simply add the results of each component:

30+80+48=15830 + 80 + 48 = 158

Q: What is the importance of calculating surface area?

A: Calculating the surface area of a rectangular prism is an important concept in mathematics and has various real-world applications, including:

  • Architecture: Engineers need to calculate the surface area of buildings to determine the amount of materials required for construction.
  • Manufacturing: Companies need to calculate the surface area of products to determine the amount of packaging materials required.
  • Packaging: Companies need to calculate the surface area of products to determine the amount of packaging materials required.
  • Design: Designers need to calculate the surface area of products to determine the amount of materials required for production.

Q: What are some real-world examples of calculating surface area?

A: Some real-world examples of calculating surface area include:

  • Building design: Architects need to calculate the surface area of buildings to determine the amount of materials required for construction.
  • Product packaging: Companies need to calculate the surface area of products to determine the amount of packaging materials required.
  • Material estimation: Engineers need to calculate the surface area of materials to determine the amount of materials required for a project.
  • Design optimization: Designers need to calculate the surface area of products to determine the most efficient design.

Q: How can I practice calculating surface area?

A: You can practice calculating surface area by:

  • Using online calculators: There are many online calculators available that can help you calculate surface area.
  • Using real-world examples: Use real-world examples, such as building design or product packaging, to practice calculating surface area.
  • Creating your own problems: Create your own problems to practice calculating surface area.
  • Working with a tutor: Work with a tutor or teacher to practice calculating surface area.

Conclusion

Calculating the surface area of a rectangular prism is an important concept in mathematics and has various real-world applications. By understanding the formula and individual components, you can calculate the surface area of a rectangular prism and apply it to real-world problems.