To interpret the notation [tex]\( v(3) = 27 \)[/tex] in the context of the volume of a cube, let's consider what the notation [tex]\( v(s) \)[/tex] represents.
- The function [tex]\( v(s) \)[/tex] represents the volume of a cube as a function of the side length [tex]\( s \)[/tex].
- The equation [tex]\( v(3) = 27 \)[/tex] states that when the side length [tex]\( s \)[/tex] of the cube is 3 feet, the volume ([tex]\( v \)[/tex]) is 27 cubic feet.
Now, let's evaluate the given options one by one:
Option A: "3 sides of the cube have a total length of 27 feet."
- This option suggests that three sides of the cube add up to 27 feet. However, the cube has only one side length measurement repeated for all sides, and no sides are added together in this context.
Option B: "3 of these cubes will have a total volume of 27 cubic feet."
- This option suggests that the volume given is for three cubes combined. However, the notation [tex]\( v(3) = 27 \)[/tex] specifically refers to one cube with side length 3 feet.
Option C: "A cube with side lengths of 3 feet has a volume of 27 cubic feet."
- This option correctly interprets the notation. If the side length [tex]\( s \)[/tex] of a cube is 3 feet, then the volume [tex]\( v(s) \)[/tex] is 3 cubed, which equals 27 cubic feet.
Option D: "A cube with a volume of 3 cubic feet has side lengths of 27 feet."
- This option incorrectly states the relationship between volume and side length. It implies an incorrect interpretation of the volume formula.
Therefore, the best interpretation of [tex]\( v(3) = 27 \)[/tex] is:
Option C: "A cube with side lengths of 3 feet has a volume of 27 cubic feet."
