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# Geometry problem

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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.

Apr 13, 2022

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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.

Apr 13, 2022