A paperback book has a length of 6 in, a width of 9 in, and a height of 3 in. A book key chain is a 1/3 scale model of the book. What is the surface area ratio of the key chain to the book? *

Answers

3

9

1/3

1/9

Since the surface area of a prism is

A = 2lw + 2lh + 2wh

then the surface of the 1/3 scale key chain will be:

A = 2 (l / 3) (w / 3) + 2 (l / 3) (h / 3) + 2 (w / 3) (h / 3)

A = (2/9) (lw) + (2 / 9) (lh) + (2/9) (wh)

A = (1 / 9) (lw + 2lh + 2wh)

so the ratio of the key chain to the book is 1/9