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.
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.
3 answers
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.
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.