Sure, let's solve this step-by-step:
1. Given Data:
- Volume of the cubical box: [tex]\( 19683 \, \text{cm}^3 \)[/tex]
2. Formula for the volume of a cube:
The volume [tex]\( V \)[/tex] of a cube with side length [tex]\( s \)[/tex] is given by:
[tex]\[
V = s^3
\][/tex]
3. Find the side length in centimeters:
To find the side length [tex]\( s \)[/tex] in centimeters, we solve for [tex]\( s \)[/tex] from the volume formula:
[tex]\[
s = \sqrt[3]{V} = \sqrt[3]{19683 \, \text{cm}^3}
\][/tex]
Evaluating the cube root of [tex]\( 19683 \, \text{cm}^3 \)[/tex], we get:
[tex]\[
s \approx 26.999999999999996 \, \text{cm}
\][/tex]
4. Convert the side length to meters:
Since [tex]\( 1 \, \text{meter} = 100 \, \text{centimeters} \)[/tex], we need to convert the side length from centimeters to meters:
[tex]\[
s \, \text{(in meters)} = \frac{s \, \text{(in centimeters)}}{100}
\][/tex]
[tex]\[
s \, \text{(in meters)} = \frac{26.999999999999996 \, \text{cm}}{100}
\][/tex]
[tex]\[
s \approx 0.26999999999999996 \, \text{meters}
\][/tex]
Thus, the length of the side of the cubical box in meters is approximately [tex]\( 0.27 \)[/tex] meters.
