To determine the side length [tex]\( s \)[/tex] of a cube with a given volume [tex]\( V \)[/tex], we use the function [tex]\( s(V) = \sqrt[3]{V} \)[/tex]. Here, we're given that the volume [tex]\( V \)[/tex] must be at least 64 cubic centimeters. Let's find the side length [tex]\( s \)[/tex] for this volume.
1. Calculate the side length for the minimum volume:
[tex]\[ s = \sqrt[3]{64} \][/tex]
2. Evaluate the cube root of 64:
[tex]\[ \sqrt[3]{64} = 4 \][/tex]
Therefore, if the volume of the cube is 64 cubic centimeters, the side length [tex]\( s \)[/tex] would be 4 centimeters.
3. Determine the reasonable range for [tex]\( s \)[/tex]:
- Since we have calculated that [tex]\( s = 4 \)[/tex] when [tex]\( V = 64 \)[/tex],
- And since [tex]\( V \)[/tex] is required to be at least 64 cubic centimeters, the side length [tex]\( s \)[/tex] cannot be less than 4 centimeters.
Consequently, the reasonable range for [tex]\( s \)[/tex] is:
[tex]\[ s \geq 4 \][/tex]
So, the appropriate range for the side length [tex]\( s \)[/tex] of Jason's cube is:
[tex]\[ s \geq 4 \][/tex]
