Comparison of Surface Areas

Oct 13, 2025 by recoveryshake.com 143 views

**Two Boxes: A Comparative Analysis of Surface Area** =====================================================

Introduction

In this article, we will delve into the world of geometry and explore the concept of surface area. We will be comparing the surface areas of two right rectangular prisms, Box A and Box B, to determine how much greater the surface area of Box B is than Box A.

Box A: Dimensions and Surface Area

Box A is a right rectangular prism with the following dimensions:

Height (h): 5 inches
Width (w): 8 inches
Depth (d): 13 inches

To calculate the surface area of Box A, we need to find the areas of all six faces and add them together. The formula for the surface area of a rectangular prism is:

SA = 2lw + 2lh + 2wd

where SA is the surface area, l is the length, w is the width, and h is the height.

For Box A, the surface area is:

SA = 2(8)(13) + 2(5)(13) + 2(8)(5) SA = 208 + 130 + 80 SA = 418 square inches

Box B: Dimensions and Surface Area

Box B is a right rectangular prism with the following dimensions:

Height (h): 8 inches
Width (w): 6 inches
Depth (d): 12 inches

Using the same formula as before, we can calculate the surface area of Box B:

SA = 2(6)(12) + 2(8)(12) + 2(6)(8) SA = 144 + 192 + 96 SA = 432 square inches

Comparison of Surface Areas

Now that we have calculated the surface areas of both Box A and Box B, we can compare them to determine how much greater the surface area of Box B is than Box A.

The difference in surface area between Box B and Box A is:

432 - 418 = 14 square inches

Therefore, the surface area of Box B is 14 square inches greater than the surface area of Box A.

Q&A

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

A: The formula for the surface area of a rectangular prism is SA = 2lw + 2lh + 2wd, where SA is the surface area, l is the length, w is the width, and h is the height.

Q: How do you calculate the surface area of a rectangular prism?

A: To calculate the surface area of a rectangular prism, you need to find the areas of all six faces and add them together.

Q: What are the dimensions of Box A?

A: The dimensions of Box A are height (h) = 5 inches, width (w) = 8 inches, and depth (d) = 13 inches.

Q: What are the dimensions of Box B?

A: The dimensions of Box B are height (h) = 8 inches, width (w) = 6 inches, and depth (d) = 12 inches.

Q: How much greater is the surface area of Box B than Box A?

A: The surface area of Box B is 14 square inches greater than the surface area of Box A.

Q: What is the surface area of Box A?

A: The surface area of Box A is 418 square inches.

Q: What is the surface area of Box B?

A: The surface area of Box B is 432 square inches.

Q: How do you find the difference in surface area between two rectangular prisms?

A: To find the difference in surface area between two rectangular prisms, you need to subtract the surface area of one prism from the surface area of the other prism.

Q: What is the formula for the surface area of a rectangular prism in terms of the dimensions?

A: The formula for the surface area of a rectangular prism in terms of the dimensions is SA = 2lw + 2lh + 2wd, where SA is the surface area, l is the length, w is the width, and h is the height.

Q: Can you give an example of how to use the formula to calculate the surface area of a rectangular prism?

A: Yes, for example, if the dimensions of a rectangular prism are length (l) = 10 inches, width (w) = 5 inches, and height (h) = 8 inches, the surface area would be SA = 2(10)(5) + 2(5)(8) + 2(10)(8) = 100 + 80 + 160 = 340 square inches.

Q: What is the significance of the surface area of a rectangular prism?

A: The surface area of a rectangular prism is significant because it represents the total area of the surface of the prism. It is an important concept in geometry and is used in various applications such as architecture, engineering, and design.

Q: Can you give an example of how the surface area of a rectangular prism is used in real-life applications?

A: Yes, for example, in architecture, the surface area of a building is used to determine the amount of materials needed for construction, such as roofing materials, siding, and insulation. In engineering, the surface area of a machine or a device is used to determine the amount of heat that is transferred or the amount of energy that is required to operate the device.