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?
Book A will require less wrapping paper because its surface area is 1.5 in.2
less than the surface area of Book B.
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 B will require less wrapping paper because its surface area is 1.5 in.2
less than the surface area of Book A.
To calculate the surface area of Book A, we need to find the area of each side of the book and add them together.
- The front and back sides have a height of 8.5 inches and a width of 1 inch, so the area of each side is 8.5 in x 1 in = 8.5 in². Since there are 2 sides, the total area for the front and back is 2 x 8.5 in² = 17 in².
- The top and bottom sides have a length of 6.5 inches and a width of 1 inch, so the area of each side is 6.5 in x 1 in = 6.5 in². Since there are 2 sides, the total area for the top and bottom is 2 x 6.5 in² = 13 in².
- The left and right sides have a length of 6.5 inches and a height of 8.5 inches, so the area of each side is 6.5 in x 8.5 in = 55.25 in². Since there are 2 sides, the total area for the left and right is 2 x 55.25 in² = 110.5 in².
To find the total surface area of Book A, we add together the areas of all sides: 17 in² + 13 in² + 110.5 in² = 140.5 in².
Similarly, to calculate the surface area of Book B:
- The front and back sides have a height of 8 inches and a width of 2 inches, so the area of each side is 8 in x 2 in = 16 in². Since there are 2 sides, the total area for the front and back is 2 x 16 in² = 32 in².
- The top and bottom sides have a length of 5.5 inches and a width of 2 inches, so the area of each side is 5.5 in x 2 in = 11 in². Since there are 2 sides, the total area for the top and bottom is 2 x 11 in² = 22 in².
- The left and right sides have a length of 5.5 inches and a height of 8 inches, so the area of each side is 5.5 in x 8 in = 44 in². Since there are 2 sides, the total area for the left and right is 2 x 44 in² = 88 in².
To find the total surface area of Book B, we add together the areas of all sides: 32 in² + 22 in² + 88 in² = 142 in².
Therefore, Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B.
are you sure?
Apologies for the mistake in my previous response. Let's calculate the surface areas of Book A and Book B correctly:
For Book A:
- The front and back sides have a length of 6.5 inches and a height of 8.5 inches, so the area of each side is 6.5 in x 8.5 in = 55.25 in². Since there are 2 sides, the total area for the front and back is 2 x 55.25 in² = 110.5 in².
- The top and bottom sides have a length of 6.5 inches and a width of 1 inch, so the area of each side is 6.5 in x 1 in = 6.5 in². Since there are 2 sides, the total area for the top and bottom is 2 x 6.5 in² = 13 in².
- The left and right sides have a height of 8.5 inches and a width of 1 inch, so the area of each side is 8.5 in x 1 in = 8.5 in². Since there are 2 sides, the total area for the left and right is 2 x 8.5 in² = 17 in².
Therefore, the total surface area of Book A is 110.5 in² + 13 in² + 17 in² = 140.5 in².
For Book B:
- The front and back sides have a length of 5.5 inches and a height of 8.0 inches, so the area of each side is 5.5 in x 8.0 in = 44 in². Since there are 2 sides, the total area for the front and back is 2 x 44 in² = 88 in².
- The top and bottom sides have a length of 5.5 inches and a width of 2 inches, so the area of each side is 5.5 in x 2 in = 11 in². Since there are 2 sides, the total area for the top and bottom is 2 x 11 in² = 22 in².
- The left and right sides have a height of 8.0 inches and a width of 2 inches, so the area of each side is 8.0 in x 2 in = 16 in². Since there are 2 sides, the total area for the left and right is 2 x 16 in² = 32 in².
Therefore, the total surface area of Book B is 88 in² + 22 in² + 32 in² = 142 in².
Consequently, Book A will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book B.