To find the length of the side of a cubical box given its volume, we can follow these steps:
1. Identify the given volume: The volume of the cubical box is [tex]\(19,683 \, \text{cm}^3\)[/tex].
2. Understand the relationship between volume and side length in a cube: The volume [tex]\( V \)[/tex] of a cube is given by:
[tex]\[
V = \text{side length}^3
\][/tex]
Let [tex]\( s \)[/tex] be the side length of the cube. Then:
[tex]\[
s^3 = 19,683 \, \text{cm}^3
\][/tex]
3. Find the cube root of the volume: To find the side length [tex]\( s \)[/tex], we take the cube root of the volume:
[tex]\[
s = \sqrt[3]{19,683 \, \text{cm}^3}
\][/tex]
4. Calculate the cube root: The cube root of [tex]\( 19,683 \, \text{cm}^3 \)[/tex] is approximately [tex]\( 27 \, \text{cm} \)[/tex]. Therefore:
[tex]\[
s = 27 \, \text{cm}
\][/tex]
5. Convert the side length from centimeters to meters:
[tex]\[
\text{Side length in meters} = \frac{27 \, \text{cm}}{100} = 0.27 \, \text{m}
\][/tex]
Hence, the length of each side of the cubical box is [tex]\( 27 \, \text{cm} \)[/tex] or [tex]\( 0.27 \, \text{m} \)[/tex].
