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 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 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 A will require less wrapping paper because its surface area is 32.75 in.2
less than the surface area of Book B.
To calculate the surface area of a rectangular prism, we add up the areas of all six sides.
For Book A:
Surface Area = 2(length*width) + 2(length*height) + 2(width*height)
Surface Area = 2(6.5*1) + 2(6.5*8.5) + 2(1*8.5)
Surface Area = 2(6.5) + 2(55.25) + 2(8.5)
Surface Area = 13 + 110.5 + 17
Surface Area = 140.5 in.²
For Book B:
Surface Area = 2(length*width) + 2(length*height) + 2(width*height)
Surface Area = 2(5.5*2) + 2(5.5*8) + 2(2*8)
Surface Area = 2(11) + 2(44) + 2(16)
Surface Area = 22 + 88 + 32
Surface Area = 142 in.²
Therefore, Book B will require less wrapping paper because its surface area is 1.5 in² less than the surface area of Book A.