To determine which book will require less wrapping paper, we need to calculate the surface area of both Book A and Book B.
The formula for the surface area \( SA \) of a rectangular prism is:
\[ SA = 2lw + 2lh + 2wh \]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Calculation for Book A:
- Length = 6.5 inches
- Width = 1 inch
- Height = 8.5 inches
\[ SA_A = 2(6.5 \times 1) + 2(6.5 \times 8.5) + 2(1 \times 8.5) \]
Calculating each term:
- \( 2(6.5 \times 1) = 2(6.5) = 13 \)
- \( 2(6.5 \times 8.5) = 2(55.25) = 110.5 \)
- \( 2(1 \times 8.5) = 2(8.5) = 17 \)
Now sum these values:
\[ SA_A = 13 + 110.5 + 17 = 140.5 \text{ in}^2 \]
Calculation for Book B:
- Length = 5.5 inches
- Width = 2 inches
- Height = 8 inches
\[ SA_B = 2(5.5 \times 2) + 2(5.5 \times 8) + 2(2 \times 8) \]
Calculating each term:
- \( 2(5.5 \times 2) = 2(11) = 22 \)
- \( 2(5.5 \times 8) = 2(44) = 88 \)
- \( 2(2 \times 8) = 2(16) = 32 \)
Now sum these values:
\[ SA_B = 22 + 88 + 32 = 142 \text{ in}^2 \]
Comparing Surface Areas:
- Surface area of Book A: \( 140.5 \text{ in}^2 \)
- Surface area of Book B: \( 142 \text{ in}^2 \)
Now, we subtract the surface areas:
\[ SA_B - SA_A = 142 - 140.5 = 1.5 \text{ in}^2 \]
Thus, Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B.
Conclusion:
Book A will require less wrapping paper because its surface area is 1.5 in.² less than the surface area of Book B.