Question

the function $s(v) = \sqrt3{v}$ describes the side length, in units, of a cube with a volume of $v$ cubic units. jason wants to build a cube with a minimum of 64 cubic centimeters. what is a reasonable range for $s$, the side length, in centimeters, of jason’s cube? $s > 0$ $s \geq 4$ $s \geq 8$ $s \geq 16$

Explanation:

Step1: Find minimum side length

Given \( V \geq 64 \) (since minimum volume is 64 cubic cm) and \( s(V)=\sqrt[3]{V} \). Substitute \( V = 64 \) into the function: \( s(64)=\sqrt[3]{64}=4 \) (because \( 4^3 = 64 \)).

Step2: Determine the range of \( s \)

Since volume \( V \) of a cube is non - negative and here \( V\geq64 \), and the side length \( s=\sqrt[3]{V} \) is an increasing function (as the cube root function is increasing for all real numbers). So when \( V\geq64 \), \( s=\sqrt[3]{V}\geq\sqrt[3]{64} = 4 \). Also, side length of a cube must be positive, but since we have a minimum volume of 64, the lower bound is 4 and it can increase as volume increases. So the range of \( s \) is \( s\geq4 \).

Answer:

B. \( s \geq 4 \) (assuming the option with \( s\geq4 \) is labeled as B, if the original options had labels, we use the correct label with the text. Here we assume the second option is \( s\geq4 \))