To determine which book requires less wrapping paper, we need to calculate the surface area for each book.
The formula for the surface area \( S \) of a rectangular prism (box) is:
\[ S = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
Surface Area Calculation for Book A
- Length (l): 6.5 inches
- Width (w): 1 inch
- Height (h): 8.5 inches
\[ S_A = 2(lw + lh + wh) \] \[ S_A = 2((6.5 \times 1) + (6.5 \times 8.5) + (1 \times 8.5)) \] \[ S_A = 2((6.5) + (55.25) + (8.5)) \] \[ S_A = 2(6.5 + 55.25 + 8.5) = 2(70.25) \] \[ S_A = 140.5 , \text{in}^2 \]
Surface Area Calculation for Book B
- Length (l): 5.5 inches
- Width (w): 2 inches
- Height (h): 8 inches
\[ S_B = 2(lw + lh + wh) \] \[ S_B = 2((5.5 \times 2) + (5.5 \times 8) + (2 \times 8)) \] \[ S_B = 2((11) + (44) + (16)) \] \[ S_B = 2(11 + 44 + 16) = 2(71) \] \[ S_B = 142 , \text{in}^2 \]
Comparison of Surface Areas
- Surface area of Book A: 140.5 in²
- Surface area of Book B: 142 in²
Conclusion
Book A requires less wrapping paper because its surface area (140.5 in²) is 1.5 in² less than the surface area of Book B (142 in²).
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.