To determine which book requires less wrapping paper, we need to calculate the surface area of each book using the formula for the surface area of a rectangular prism:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \(l\) is the length, \(w\) is the width, and \(h\) is the height.
For Book A:
- Length \(l = 6.5\) inches
- Width \(w = 1\) inch
- Height \(h = 8.5\) inches
\[ \text{Surface Area of Book A} = 2(6.5 \times 1 + 6.5 \times 8.5 + 1 \times 8.5) \] \[ = 2(6.5 + 55.25 + 8.5) \] \[ = 2(70.25) = 140.5 \text{ in}^2 \]
For Book B:
- Length \(l = 5.5\) inches
- Width \(w = 2\) inches
- Height \(h = 8\) inches
\[ \text{Surface Area of Book B} = 2(5.5 \times 2 + 5.5 \times 8 + 2 \times 8) \] \[ = 2(11 + 44 + 16) \] \[ = 2(71) = 142 \text{ in}^2 \]
Now let's compare the surface areas:
- Surface Area of Book A: \(140.5 \text{ in}^2\)
- Surface Area of Book B: \(142 \text{ in}^2\)
Since \(140.5 < 142\), Book A requires less wrapping paper.
The correct response is: Book A will require less wrapping paper because its surface area is 1.5 in.² less than the surface area of Book B.