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 rectangular box (or cuboid) is:
\[ SA = 2(lw + lh + wh) \]
where:
- \( l \) = length
- \( w \) = width
- \( h \) = height
Calculating for Book A:
- Length \( l = 6.5 \) inches,
- Width \( w = 1 \) inch,
- Height \( h = 8.5 \) inches.
\[ SA_A = 2(6.5 \cdot 1 + 6.5 \cdot 8.5 + 1 \cdot 8.5) \]
Calculating the individual areas:
- \( lw = 6.5 \cdot 1 = 6.5 \)
- \( lh = 6.5 \cdot 8.5 = 55.25 \)
- \( wh = 1 \cdot 8.5 = 8.5 \)
Now, sum these areas: \[ 6.5 + 55.25 + 8.5 = 70.25 \]
Now calculate the surface area: \[ SA_A = 2 \cdot 70.25 = 140.5 , \text{in}^2 \]
Calculating for Book B:
- Length \( l = 5.5 \) inches,
- Width \( w = 2 \) inches,
- Height \( h = 8 \) inches.
\[ SA_B = 2(5.5 \cdot 2 + 5.5 \cdot 8 + 2 \cdot 8) \]
Calculating the individual areas:
- \( lw = 5.5 \cdot 2 = 11 \)
- \( lh = 5.5 \cdot 8 = 44 \)
- \( wh = 2 \cdot 8 = 16 \)
Now, sum these areas: \[ 11 + 44 + 16 = 71 \]
Now calculate the surface area: \[ SA_B = 2 \cdot 71 = 142 , \text{in}^2 \]
Comparing Surface Areas:
- Surface area of Book A: \( 140.5 , \text{in}^2 \)
- Surface area of Book B: \( 142 , \text{in}^2 \)
Since \( 140.5 < 142 \), Book A requires less wrapping paper.
Now, calculating the difference in surface areas: \[ 142 - 140.5 = 1.5 , \text{in}^2 \]
Thus, 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.
0 answers