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 (box) is given by:
\[ S = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Calculating the surface area of Book A:
- Length \( l = 6.5 \) inches
- Width \( w = 1 \) inch
- Height \( h = 8.5 \) inches
\[ S_A = 2(lw + lh + wh) = 2(6.5 \cdot 1 + 6.5 \cdot 8.5 + 1 \cdot 8.5) \]
Calculating each term:
- \( lw = 6.5 \times 1 = 6.5 \)
- \( lh = 6.5 \times 8.5 = 55.25 \)
- \( wh = 1 \times 8.5 = 8.5 \)
Now summing these values: \[ S_A = 2(6.5 + 55.25 + 8.5) = 2(70.25) = 140.5 , \text{in}^2 \]
Calculating the surface area of Book B:
- Length \( l = 5.5 \) inches
- Width \( w = 2 \) inches
- Height \( h = 8 \) inches
\[ S_B = 2(lw + lh + wh) = 2(5.5 \cdot 2 + 5.5 \cdot 8 + 2 \cdot 8) \]
Calculating each term:
- \( lw = 5.5 \times 2 = 11 \)
- \( lh = 5.5 \times 8 = 44 \)
- \( wh = 2 \times 8 = 16 \)
Now summing these values: \[ S_B = 2(11 + 44 + 16) = 2(71) = 142 , \text{in}^2 \]
Comparing the surface areas:
- Surface area of Book A: \( 140.5 , \text{in}^2 \)
- Surface area of Book B: \( 142 , \text{in}^2 \)
Since \( 140.5 , \text{in}^2 < 142 , \text{in}^2 \), Book A has a smaller surface area and thus will require less wrapping paper.
The correct response is:
Book A will require less wrapping paper because its surface area is 1.5 in.² less than the surface area of Book B.
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