Central Limit Theorem with Volume

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Suppose are growing limes. Suppose the mean radius of the limes is 9cm with standard deviation 2 cm. Suppose a bar who will buy our limes expects the volume of the limes to be between 8π cm3 and 12π cm3. If they will buy 6 dozen limes, what is the probability the sample mean volume will be in this range? I am stack with volume, thinking to use volume of sphere to find radius. Please help.