What is the exterior surface area, in square inches, of a box without a lid, if the length of each edge is 29 inches?
Understand the Problem
The question is asking for the calculation of the exterior surface area of a box that is square and does not have a lid, given that the length of each edge is 29 inches. To solve this, we will use the formula for the surface area of a square box, accounting for the fact that it lacks a lid.
Answer
The exterior surface area of the box without a lid is \( 4205 \) square inches.
Answer for screen readers
The total exterior surface area of the box without a lid is ( 4205 ) square inches.
Steps to Solve
- Identify the components of the box
Since the box is square and does not have a lid, it has a square base and four vertical sides.
- Calculate the area of the base
The area of the base, which is a square, can be calculated using the formula for the area of a square:
$$ \text{Area of the base} = \text{side}^2 = 29^2 = 841 \text{ square inches} $$
- Calculate the area of the sides
Each side is a rectangle with width equal to the edge length (29 inches) and height equal to the side’s length. The area of one side is:
$$ \text{Area of one side} = \text{base} \times \text{height} = 29 \times 29 = 841 \text{ square inches} $$
Since there are four sides, the total area of the sides is:
$$ \text{Total area of sides} = 4 \times 841 = 3364 \text{ square inches} $$
- Total exterior surface area calculation
To find the total exterior surface area of the box without a lid, add the area of the base and the total area of the sides:
$$ \text{Total surface area} = \text{Area of the base} + \text{Total area of sides} = 841 + 3364 = 4205 \text{ square inches} $$
The total exterior surface area of the box without a lid is ( 4205 ) square inches.
More Information
The surface area calculation is important in various real-life applications such as packaging, material requirements, and even in construction. Understanding how the area is computed can help with practical problem-solving skills.
Tips
- Forgetting to include the area of the base when the box does not have a lid.
- Incorrectly calculating the dimensions of the rectangular sides.
- Misremembering the formula for the area of a square or rectangle.
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