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Sue is wrapping books to give as gifts. Book A has a length of 6.5 inches, a width of 1 inch, and a height of 8.5 inches. Book B has a length of 5.5 inches, a width of 2 inches, and a height of 8 inches. Based on surface area, which book will require less wrapping paper?(1 point) Responses Book A will require less wrapping paper because its surface area is 32.75 in.2 less than the surface area of Book B. Book A will require less wrapping paper because its surface area is 32.75 in.2 less than the surface area of Book B. Book B will require less wrapping paper because its surface area is 1.5 in.2 less than the surface area of Book A. Book B will require less wrapping paper because its surface area is 1.5 in.2 less than the surface area of Book A. Book B will require less wrapping paper because its surface area is 0.5 in.2 less than the surface area of Book A. Book B will require less wrapping paper because its surface area is 0.5 in.2 less than the surface area of Book A. Book A will require less wrapping paper because its surface area is 1.5 in.2 less than the surface area of Book B.

1 answer

To determine which book requires less wrapping paper, we need to calculate the surface area of each book.

The formula for the surface area \( S \) of a rectangular prism (box) is: \[ S = 2(lw + lh + wh) \]

Where:

  • \( l \) = length
  • \( w \) = width
  • \( h \) = height

Book A:

  • Length = 6.5 inches
  • Width = 1 inch
  • Height = 8.5 inches

Calculating the surface area: \[ S_A = 2(6.5 \cdot 1 + 6.5 \cdot 8.5 + 1 \cdot 8.5) \] \[ = 2(6.5 + 55.25 + 8.5) \] \[ = 2(70.25) \] \[ = 140.5 \text{ in}^2 \]

Book B:

  • Length = 5.5 inches
  • Width = 2 inches
  • Height = 8 inches

Calculating the surface area: \[ S_B = 2(5.5 \cdot 2 + 5.5 \cdot 8 + 2 \cdot 8) \] \[ = 2(11 + 44 + 16) \] \[ = 2(71) \] \[ = 142 \text{ in}^2 \]

Comparing Surface Areas:

  • Surface Area of Book A = 140.5 in²
  • Surface Area of Book B = 142 in²

Conclusion:

Book A has a surface area of 140.5 in², while Book B has a surface area of 142 in². Therefore, Book A will require less wrapping paper because its surface area is 1.5 in.² less than the surface area of Book B.