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 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 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 A will require less wrapping paper because its surface area is 1.5 in.2 less than the surface area of Book B.
To calculate the surface area of a rectangular prism, we use the formula:
Surface Area = 2(length × width) + 2(length × height) + 2(width × height)
For Book A:
Surface Area = 2(6.5 × 1) + 2(6.5 × 8.5) + 2(1 × 8.5)
Surface Area = 13 + 110.5 + 17
Surface Area = 140.5 in²
For Book B:
Surface Area = 2(5.5 × 2) + 2(5.5 × 8) + 2(2 × 8)
Surface Area = 22 + 88 + 32
Surface Area = 142 in²
Therefore, Book B will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book A.