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Shiloh wants to create a paper-mâché box shaped like a rectangular prism. If the box will be 4 inches by 5 inches by 8 inches, how much paper does she need to cover the box?

Ask by Norris Lewis. in the United States
Mar 13,2025

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Tutor-Verified Answer

Answer

Shiloh needs 184 square inches of paper to cover the box.

Solution

The paper needed is equal to the surface area of the box. 1. The box is a rectangular prism with dimensions \(4\) inches, \(5\) inches, and \(8\) inches. 2. The formula for the surface area \(S\) of a rectangular prism is: \[ S = 2(ab + ac + bc) \] where \(a\), \(b\), and \(c\) are the dimensions. 3. Substitute the dimensions into the formula: \[ S = 2((4 \times 5) + (4 \times 8) + (5 \times 8)) \] 4. Calculate each product: \[ 4 \times 5 = 20,\quad 4 \times 8 = 32,\quad 5 \times 8 = 40 \] 5. Add the products: \[ 20 + 32 + 40 = 92 \] 6. Multiply by \(2\) to get the total surface area: \[ 2 \times 92 = 184 \] Therefore, Shiloh needs paper to cover \(\boxed{184}\) square inches of the box.

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Beyond the Answer

To find out how much paper Shiloh needs to cover the box, we need to calculate the surface area of the rectangular prism. The surface area (SA) can be found using the formula: SA = 2(lw + lh + wh), where l = length, w = width, and h = height. For the box dimensions of 4 inches (w), 5 inches (l), and 8 inches (h), we have: SA = 2(4 * 5 + 4 * 8 + 5 * 8) = 2(20 + 32 + 40) = 2(92) = 184 square inches. So, Shiloh will need 184 square inches of paper to cover her box. Happy crafting! To make this experience even more enjoyable, consider using old newspapers or magazines for her paper-mâché project. Not only does it give a unique design to the box, but it's also an eco-friendly way to recycle materials. Plus, the different patterns and colors can create a fun artistic flair! Additionally, while working on this project, ensure that Shiloh has her work area covered with a plastic sheet or newspapers to avoid any mess. Paper-mâché glue can be sticky, and it's easy to accidentally spill some! Having cleaning supplies handy will make cleanup after this creative adventure a breeze.

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