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)

Question

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 will require less wrapping paper, we need to calculate the surface area of each book.

The surface area $S$ of a rectangular prism (which a book can be approximated as) can be calculated using the formula: $$S=2(lw+lh+wh)$$ where $l$ = length, $w$ = width, and $h$ = height.

For Book A:

• Length $l=6.5$ in
• Width $w=1$ in
• Height $h=8.5$ in

Calculating the surface area of Book A: $$S_A=2(6.5\times 1+6.5\times 8.5+1\times 8.5)$$

Calculating each term:

1. $6.5\times 1=6.5$
2. $6.5\times 8.5=55.25$
3. $1\times 8.5=8.5$

Adding these results: $$S_A=2(6.5+55.25+8.5)=2(70.25)=140.5{\text{ in}}^2$$

For Book B:

• Length $l=5.5$ in
• Width $w=2$ in
• Height $h=8$ in

Calculating the surface area of Book B: $$S_B=2(5.5\times 2+5.5\times 8+2\times 8)$$

Calculating each term:

1. $5.5\times 2=11$
2. $5.5\times 8=44$
3. $2\times 8=16$

Adding these results: $$S_B=2(11+44+16)=2(71)=142{\text{ in}}^2$$

Now we can compare the surface areas:

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

Since 140.5 in² is less than 142 in², Book A will require less wrapping paper.

The correct response is: Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B.