For Exercises 2–3, refer to the following: The area of a circle of radius is . Expressed in terms of the diameter, , the area is . If we apply a linear scaling factor to the diameter, then the area of the scaled circle—just as is the case for a square—changes with , the square of the linear scaling factor.

Question 18.33

3. The NBC Nightly News on June 21, 2010, featured a story about food portions, stating that dinner plates were 9 in. in diameter in the 1960s but now they are 12 in. in diameter, “making room for one-third more food.”

  1. What is the linear scaling factor for a 12-in. plate compared with a 9-in. plate?
  2. How many times as large in area is a 12-in. plate compared with a 9-in. plate?
  3. What percentage greater is the area of a 12-in. plate compared with a 9-in. plate?

3.

(a)

(b) 1.378

(c) 78%