To determine which book requires less wrapping paper, we need to calculate the surface area of each book. The formula for the surface area \( A \) of a rectangular prism (like a book) is:
\[ A = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the rectangular prism.
Let's calculate the surface area for Book A first:
- Length \( l_A = 6.5 \) inches
- Width \( w_A = 1 \) inch
- Height \( h_A = 8.5 \) inches
\[ A_A = 2(l_A w_A + l_A h_A + w_A h_A) \] \[ A_A = 2((6.5 \times 1) + (6.5 \times 8.5) + (1 \times 8.5)) \] \[ A_A = 2(6.5 + 55.25 + 8.5) \] \[ A_A = 2(70.25) \] \[ A_A = 140.5 \text{ square inches} \]
Now, let's calculate the surface area for Book B:
- Length \( l_B = 5.5 \) inches
- Width \( w_B = 2 \) inches
- Height \( h_B = 8 \) inches
\[ A_B = 2(l_B w_B + l_B h_B + w_B h_B) \] \[ A_B = 2((5.5 \times 2) + (5.5 \times 8) + (2 \times 8)) \] \[ A_B = 2(11 + 44 + 16) \] \[ A_B = 2(71) \] \[ A_B = 142 \text{ square inches} \]
Now we can compare the surface areas:
- Surface area of Book A: \( 140.5 \) square inches
- Surface area of Book B: \( 142 \) square inches
Since \( 140.5 < 142 \), Book A will require less wrapping paper.