To find out how many times larger the volume of the saltwater tank is compared to the freshwater tank, we first need to calculate the volumes of both tanks.
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Volume of the freshwater tank: \[ V_{freshwater} = \text{side length}^3 = 15 , \text{cm}^3 = 15^3 = 3375 , \text{cm}^3 \]
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Volume of the saltwater tank: \[ V_{saltwater} = \text{side length}^3 = 45 , \text{cm}^3 = 45^3 = 91125 , \text{cm}^3 \]
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Now, to find how many times larger the volume of the saltwater tank is compared to the freshwater tank: \[ \text{Ratio} = \frac{V_{saltwater}}{V_{freshwater}} = \frac{91125}{3375} \]
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Calculating the ratio: \[ \frac{91125}{3375} = 27 \]
Thus, the volume of the saltwater tank is 27 times larger than the volume of the freshwater tank.
The answer is 27.