To determine which book requires less wrapping paper, we need to calculate the surface area of both books. The formula for the surface area \( S \) of a rectangular box is given by:
\[ S = 2(lw + lh + wh) \]
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:
\[ S_A = 2((6.5 \times 1) + (6.5 \times 8.5) + (1 \times 8.5)) \]
Calculating each term:
- \( 6.5 \times 1 = 6.5 \)
- \( 6.5 \times 8.5 = 55.25 \)
- \( 1 \times 8.5 = 8.5 \)
Adding them together: \[ 6.5 + 55.25 + 8.5 = 70.25 \]
Now multiplying by 2 for the surface area: \[ S_A = 2 \times 70.25 = 140.5 \text{ in}^2 \]
For Book B:
- Length \( l = 5.5 \) inches
- Width \( w = 2 \) inches
- Height \( h = 8 \) inches
Calculating the surface area:
\[ S_B = 2((5.5 \times 2) + (5.5 \times 8) + (2 \times 8)) \]
Calculating each term:
- \( 5.5 \times 2 = 11 \)
- \( 5.5 \times 8 = 44 \)
- \( 2 \times 8 = 16 \)
Adding them together: \[ 11 + 44 + 16 = 71 \]
Now multiplying by 2 for the surface area: \[ S_B = 2 \times 71 = 142 \text{ in}^2 \]
Conclusion:
- Surface area of Book A: \( 140.5 \text{ in}^2 \)
- Surface area of Book B: \( 142 \text{ in}^2 \)
Based on this calculation, Book A has a smaller surface area than Book B, therefore:
Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B.