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 32.75 in.^2. less than the surface area of Book B.
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.
c Book B will require less wrapping paper because its surface area is 0.5 in.^2 less than the surface area of Book A.
d 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 determine the surface area of each book, we need to calculate the area of each side and then sum them up.
For Book A, the surface area is calculated as follows:
Side 1: Length * Width = 6.5 in * 1 in = 6.5 in^2
Side 2: Length * Width = 6.5 in * 1 in = 6.5 in^2
Side 3: Width * Height = 1 in * 8.5 in = 8.5 in^2
Side 4: Width * Height = 1 in * 8.5 in = 8.5 in^2
Side 5: Length * Height = 6.5 in * 8.5 in = 55.25 in^2
Side 6: Length * Height = 6.5 in * 8.5 in = 55.25 in^2
Total surface area of Book A = Side 1 + Side 2 + Side 3 + Side 4 + Side 5 + Side 6 = 6.5 in^2 + 6.5 in^2 + 8.5 in^2 + 8.5 in^2 + 55.25 in^2 + 55.25 in^2 = 140 in^2
For Book B, the surface area is calculated as follows:
Side 1: Length * Width = 5.5 in * 2 in = 11 in^2
Side 2: Length * Width = 5.5 in * 2 in = 11 in^2
Side 3: Width * Height = 2 in * 8 in = 16 in^2
Side 4: Width * Height = 2 in * 8 in = 16 in^2
Side 5: Length * Height = 5.5 in * 8 in = 44 in^2
Side 6: Length * Height = 5.5 in * 8 in = 44 in^2
Total surface area of Book B = Side 1 + Side 2 + Side 3 + Side 4 + Side 5 + Side 6 = 11 in^2 + 11 in^2 + 16 in^2 + 16 in^2 + 44 in^2 + 44 in^2 = 142 in^2
Therefore, the correct answer is:
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.