To determine which book requires less wrapping paper, we need to calculate the surface areas of Book A and Book B.
The formula for the surface area \(S\) of a right rectangular prism is:
\[ S = 2(lw + lh + wh) \]
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
Calculating the surface area:
\[ S_A = 2((6.5 \times 1) + (6.5 \times 8.5) + (1 \times 8.5)) \] \[ = 2(6.5 + 55.25 + 8.5) \] \[ = 2(70.25) \] \[ = 140.5 , \text{in}^2 \]
For Book B:
- Length \(l = 5.5\) inches
- Width \(w = 2\) inches
- Height \(h = 8\) inches
Calculating the surface area:
\[ S_B = 2((5.5 \times 2) + (5.5 \times 8) + (2 \times 8)) \] \[ = 2(11 + 44 + 16) \] \[ = 2(71) \] \[ = 142 , \text{in}^2 \]
Now we 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 has a smaller surface area.
Conclusion: Book A will require less wrapping paper because its surface area is \(1.5 , \text{in}^2\) less than the surface area of Book B.
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.