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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?

a. Book A will require less wrapping paper because its surface area is 32.75in² less than the surface area of Book B
b. Book A will require less wrapping paper because its surface area is 1.5ln² less than the surface area of Book B.
c. Book 8 will require less wrapping paper because its surface area is 0.5in² less than the surface area of Book A.
d. Book B will require less wrapping paper because its surface area is 1.5ln² less than the surface area of Book A.

User Speller
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1 Answer

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Final answer:

Book A requires less wrapping paper with a surface area of 140.5in² compared to Book B's 142in², so Book A's surface area is 1.5in² less than Book B. Option b. Book A will require less wrapping paper because its surface area is 1.5ln² less than the surface area of Book B is the correct answer.

Step-by-step explanation:

The question involves comparing the surface area of two rectangular solids (books) to determine which one would require less wrapping paper. We will calculate the surface area of each book and compare them.

Calculations for Book A

To find the surface area of Book A, we calculate the area of all six faces (2lw + 2lh + 2wh) and sum them up:

  • Top/Bottom (2lw): 2 * 6.5in * 1in = 13in²
  • Front/Back (2lh): 2 * 6.5in * 8.5in = 110.5in²
  • Side (2wh): 2 * 1in * 8.5in = 17in²

Total surface area of Book A = 13in²+ 110.5in² + 17in² = 140.5in²

Calculations for Book B

To find the surface area of Book B, we again calculate the area of all six faces:

  • Top/Bottom (2lw): 2 * 5.5in * 2in = 22in²
  • Front/Back (2lh): 2 * 5.5in * 8in = 88in²
  • Side (2wh): 2 * 2in * 8in = 32in²

Total surface area of Book B = 22in² + 88in² + 32in² = 142in²

Comparison

Comparing the two surface areas:

  1. Surface area of Book A: 140.5in²
  2. Surface area of Book B: 142in²

Since Book A has a surface area of 140.5in² and Book B has a surface area of 142in², Book A will require less wrapping paper because its surface area is 1.5in² less than that of Book B.

Therefore, the correct answer is:

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

User Mrsus
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