Mrs. Read can knit one pair of children's mittens with a ball of yarn six inches in diameter. How many pairs of identical mittens can she knit with a ball of yarn 18 inches in diameter? Assume that the balls of yarn are rolled consistently.
+2666 Mrs. Read uses \(3^3 \pi {4 \over 3} = 36 \pi\) inches of yarn per mitten.
The bigger ball has a volume of \(9^3 \pi {4 \over 3} = 972 \pi\) inches of yarn per mitten.
Thus, she can make a total of \({972 \pi \over 36 \pi} = \color{brown}\boxed{27}\) mittens.
