Gift Wrapping A gift box has the shape of a rectangular prism. How much wrapping paper do you need to cover the​ box?

Question

15 in.
3 in.
16 in.
Question content area bottom
Part 1
You need
  
enter your response here in. squared of paper to cover the box.

Answer 1

To find the amount of wrapping paper needed to cover a rectangular prism, we need to calculate the surface area of the box. The formula for the surface area \(A\) of a rectangular prism is:

\[ A = 2(lw + lh + wh) \]

where:

• \(l\) = length,
• \(w\) = width,
• \(h\) = height.

From the dimensions you've provided:

• Length (\(l\)) = 15 inches,
• Width (\(w\)) = 3 inches,
• Height (\(h\)) = 16 inches.

Now, we can plug the values into the formula:

\[ A = 2(15 \cdot 3 + 15 \cdot 16 + 3 \cdot 16) \]

Calculating each part:

1. \(15 \cdot 3 = 45\)
2. \(15 \cdot 16 = 240\)
3. \(3 \cdot 16 = 48\)

Now add these results together:

\[ A = 2(45 + 240 + 48) \] \[ A = 2(333) \] \[ A = 666 \text{ square inches} \]

So, you need 666 in² of wrapping paper to cover the box.