To determine which book requires less wrapping paper based on surface area, we need to calculate the surface area for both Book A and Book B using the formula for the surface area of a rectangular prism:
\[ \text{Surface Area} = 2(lw + lh + wh) \]
where \( l \) is the length, \( w \) is the width, and \( h \) is the height.
For Book A:
- Length \( l = 6.5 \) inches
- Width \( w = 1 \) inch
- Height \( h = 8.5 \) inches
Calculating the surface area:
\[ \text{Surface Area}_A = 2(lw + lh + wh) \]
Calculating each component:
- \( lw = 6.5 \times 1 = 6.5 \)
- \( lh = 6.5 \times 8.5 = 55.25 \)
- \( wh = 1 \times 8.5 = 8.5 \)
Now, summing them up:
\[ lw + lh + wh = 6.5 + 55.25 + 8.5 = 70.25 \]
Now, calculating the total surface area:
\[ \text{Surface Area}_A = 2 \times 70.25 = 140.5 , \text{in}^2 \]
For Book B:
- Length \( l = 5.5 \) inches
- Width \( w = 2 \) inches
- Height \( h = 8 \) inches
Calculating the surface area:
\[ \text{Surface Area}_B = 2(lw + lh + wh) \]
Calculating each component:
- \( lw = 5.5 \times 2 = 11 \)
- \( lh = 5.5 \times 8 = 44 \)
- \( wh = 2 \times 8 = 16 \)
Now, summing them up:
\[ lw + lh + wh = 11 + 44 + 16 = 71 \]
Now, calculating the total surface area:
\[ \text{Surface Area}_B = 2 \times 71 = 142 , \text{in}^2 \]
Conclusion:
- Surface Area of Book A: 140.5 in²
- Surface Area of Book B: 142 in²
Book A requires less wrapping paper because its surface area is less than the surface area of Book B.
The correct option is: Book A will require less wrapping paper because its surface area is less than the surface area of Book B.