To find the volume of the pool float ducky when the dimensions of the bath time rubber ducky are multiplied by 16, we need to use the properties of similar figures.
When the dimensions of a figure are multiplied by a scale factor \( k \), the volume changes by a factor of \( k^3 \).
In this case, the scale factor is \( k = 16 \). Therefore, the volume of the pool float ducky can be calculated as follows:
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Calculate the change in volume: \[ k^3 = 16^3 = 4096 \]
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Multiply the volume of the bath time ducky by \( k^3 \): \[ \text{Volume of pool float ducky} = \text{Volume of bath time rubber ducky} \times k^3 = 486 , \text{cm}^3 \times 4096 \]
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Perform the multiplication: \[ 486 \times 4096 = 1990656 , \text{cm}^3 \]
Thus, the volume of the pool float rubber ducky is \( 1990656 , \text{cm}^3 \).