The Length Of Each Edge Of A Cubical Storage Box Is 15 Feet. What Is The Exterior Surface Area, In Square Feet, Of This Box Without A Lid? Enter Your Answer:

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Introduction

In this article, we will explore the concept of calculating the exterior surface area of a cubical storage box. The problem states that the length of each edge of the box is 15 feet, and we are asked to find the exterior surface area of the box without a lid. We will use mathematical formulas and calculations to arrive at the solution.

Understanding the Problem

To solve this problem, we need to understand the concept of surface area and how it relates to a cubical shape. A cubical shape has six faces, each of which is a square. The surface area of a cube is the sum of the areas of these six faces.

Calculating the Surface Area

The formula for the surface area of a cube is:

Surface Area = 6 × (edge length)^2

In this case, the edge length is 15 feet. Plugging this value into the formula, we get:

Surface Area = 6 × (15)^2 Surface Area = 6 × 225 Surface Area = 1350

Calculating the Surface Area Without a Lid

However, the problem asks us to find the exterior surface area of the box without a lid. This means that we need to subtract the area of the top and bottom faces from the total surface area.

The area of each face is (edge length)^2, so the area of the top and bottom faces is:

Area of top and bottom faces = 2 × (edge length)^2 Area of top and bottom faces = 2 × 225 Area of top and bottom faces = 450

Subtracting the Area of the Top and Bottom Faces

Now, we subtract the area of the top and bottom faces from the total surface area:

Exterior Surface Area = Total Surface Area - Area of top and bottom faces Exterior Surface Area = 1350 - 450 Exterior Surface Area = 900

Conclusion

In conclusion, the exterior surface area of the cubical storage box without a lid is 900 square feet.

Key Takeaways

  • The surface area of a cube is the sum of the areas of its six faces.
  • The formula for the surface area of a cube is: Surface Area = 6 × (edge length)^2.
  • To find the exterior surface area of a cube without a lid, we need to subtract the area of the top and bottom faces from the total surface area.

Real-World Applications

This problem has real-world applications in various fields such as architecture, engineering, and design. For example, when designing a building or a structure, architects and engineers need to calculate the surface area of the exterior walls to determine the amount of materials needed for construction.

Mathematical Formulas

  • Surface Area = 6 × (edge length)^2
  • Area of top and bottom faces = 2 × (edge length)^2

Glossary of Terms

  • Surface Area: The total area of the exterior surface of a three-dimensional shape.
  • Cube: A three-dimensional shape with six faces, each of which is a square.
  • Edge Length: The length of one side of a cube.

References

  • [1] "Mathematics for Engineers and Scientists" by Donald R. Hill
  • [2] "Geometry: A Comprehensive Introduction" by Dan Pedoe

Additional Resources

  • Khan Academy: Surface Area of a Cube
  • Math Open Reference: Surface Area of a Cube
  • Wolfram MathWorld: Surface Area of a Cube
    The Exterior Surface Area of a Cubical Storage Box: Q&A =====================================================

Introduction

In our previous article, we explored the concept of calculating the exterior surface area of a cubical storage box. We used mathematical formulas and calculations to arrive at the solution. In this article, we will answer some frequently asked questions related to the exterior surface area of a cubical storage box.

Q: What is the formula for the surface area of a cube?

A: The formula for the surface area of a cube is:

Surface Area = 6 × (edge length)^2

Q: How do I calculate the surface area of a cube?

A: To calculate the surface area of a cube, you need to know the length of one side of the cube (edge length). You can then plug this value into the formula:

Surface Area = 6 × (edge length)^2

Q: What is the difference between the surface area and the exterior surface area of a cube?

A: The surface area of a cube is the total area of all six faces, including the top and bottom faces. The exterior surface area of a cube is the total area of the exterior surface, excluding the top and bottom faces.

Q: How do I calculate the exterior surface area of a cube without a lid?

A: To calculate the exterior surface area of a cube without a lid, you need to subtract the area of the top and bottom faces from the total surface area. The area of each face is (edge length)^2, so the area of the top and bottom faces is:

Area of top and bottom faces = 2 × (edge length)^2

You can then subtract this value from the total surface area:

Exterior Surface Area = Total Surface Area - Area of top and bottom faces

Q: What is the exterior surface area of a cube with an edge length of 10 feet?

A: To calculate the exterior surface area of a cube with an edge length of 10 feet, you can use the formula:

Surface Area = 6 × (edge length)^2 Surface Area = 6 × (10)^2 Surface Area = 600

Since we are not including the top and bottom faces, we need to subtract the area of these faces:

Area of top and bottom faces = 2 × (edge length)^2 Area of top and bottom faces = 2 × (10)^2 Area of top and bottom faces = 200

Exterior Surface Area = Total Surface Area - Area of top and bottom faces Exterior Surface Area = 600 - 200 Exterior Surface Area = 400

Q: What is the exterior surface area of a cube with an edge length of 15 feet?

A: To calculate the exterior surface area of a cube with an edge length of 15 feet, you can use the formula:

Surface Area = 6 × (edge length)^2 Surface Area = 6 × (15)^2 Surface Area = 1350

Since we are not including the top and bottom faces, we need to subtract the area of these faces:

Area of top and bottom faces = 2 × (edge length)^2 Area of top and bottom faces = 2 × (15)^2 Area of top and bottom faces = 450

Exterior Surface Area = Total Surface Area - Area of top and bottom faces Exterior Surface Area = 1350 - 450 Exterior Surface Area = 900

Conclusion

In conclusion, we have answered some frequently asked questions related to the exterior surface area of a cubical storage box. We have provided formulas and calculations to help you understand the concept of surface area and how to calculate it.

Key Takeaways

  • The surface area of a cube is the sum of the areas of its six faces.
  • The formula for the surface area of a cube is: Surface Area = 6 × (edge length)^2.
  • To find the exterior surface area of a cube without a lid, you need to subtract the area of the top and bottom faces from the total surface area.

Real-World Applications

This problem has real-world applications in various fields such as architecture, engineering, and design. For example, when designing a building or a structure, architects and engineers need to calculate the surface area of the exterior walls to determine the amount of materials needed for construction.

Mathematical Formulas

  • Surface Area = 6 × (edge length)^2
  • Area of top and bottom faces = 2 × (edge length)^2

Glossary of Terms

  • Surface Area: The total area of the exterior surface of a three-dimensional shape.
  • Cube: A three-dimensional shape with six faces, each of which is a square.
  • Edge Length: The length of one side of a cube.

References

  • [1] "Mathematics for Engineers and Scientists" by Donald R. Hill
  • [2] "Geometry: A Comprehensive Introduction" by Dan Pedoe

Additional Resources

  • Khan Academy: Surface Area of a Cube
  • Math Open Reference: Surface Area of a Cube
  • Wolfram MathWorld: Surface Area of a Cube