To determine which book requires less wrapping paper, we need to calculate the surface area of both Book A and Book B.
The formula for the surface area \( S \) of a 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: \( 142 \text{ in}^2 \)
Conclusion: Book A has a surface area of 140.5 in², which is less than Book B's surface area of 142 in².
Therefore, the response should be:
Book A will require less wrapping paper because its surface area is 1.5 in.² less than the surface area of Book B.