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 (SA) of a right rectangular prism is given by:
\[ SA = 2lw + 2lh + 2wh \]
where:
- \( l \) is the length,
- \( w \) is the width,
- \( h \) is the height.
Calculating the surface area of Book A:
- Length (l) = 6.5 inches
- Width (w) = 1 inch
- Height (h) = 8.5 inches
\[ SA_A = 2(6.5 \cdot 1) + 2(6.5 \cdot 8.5) + 2(1 \cdot 8.5) \]
Calculating each term:
- \( 2(6.5 \cdot 1) = 13 \)
- \( 2(6.5 \cdot 8.5) = 2(55.25) = 110.5 \)
- \( 2(1 \cdot 8.5) = 17 \)
Adding these together: \[ SA_A = 13 + 110.5 + 17 = 140.5 \text{ in}^2 \]
Calculating the surface area of Book B:
- Length (l) = 5.5 inches
- Width (w) = 2 inches
- Height (h) = 8 inches
\[ SA_B = 2(5.5 \cdot 2) + 2(5.5 \cdot 8) + 2(2 \cdot 8) \]
Calculating each term:
- \( 2(5.5 \cdot 2) = 2(11) = 22 \)
- \( 2(5.5 \cdot 8) = 2(44) = 88 \)
- \( 2(2 \cdot 8) = 2(16) = 32 \)
Adding these together: \[ SA_B = 22 + 88 + 32 = 142 \text{ in}^2 \]
Comparison:
- Surface area of Book A: \( 140.5 \text{ in}^2 \)
- Surface area of Book B: \( 142 \text{ in}^2 \)
Book A has a surface area of \( 140.5 \text{ in}^2 \) and Book B has a surface area of \( 142 \text{ in}^2 \).
Thus, Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B.
So the correct response is: Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B.