Question

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.

Answer 1

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.