Sure, let's break this down step-by-step.
### Question:
The volume of a cubical box is 2744 m³. Find the length of the side of the box.
### Solution:
1. Understand the relationship: Since the box is cubical, all its sides are of equal length. If we denote the side length of the cubical box as [tex]\( s \)[/tex], then the volume of a cube is given by:
[tex]\[
\text{Volume} = s^3
\][/tex]
2. Given data: The volume of the box is provided as 2744 m³. Therefore,
[tex]\[
s^3 = 2744
\][/tex]
3. Finding the side length: To find [tex]\( s \)[/tex], we need to find the cube root of 2744. That is,
[tex]\[
s = \sqrt[3]{2744}
\][/tex]
4. Determine the cube root: The cube root of 2744 is:
[tex]\[
\sqrt[3]{2744} = 13.999999999999998
\][/tex]
5. Conclusion: The side length of the cubical box is approximately:
[tex]\[
14 \text{ meters}
\][/tex]
### Additional Task:
Find the cube root of 2197.
1. Finding the cube root: To find the cube root of 2197, we need:
[tex]\[
\sqrt[3]{2197}
\][/tex]
2. Determine the cube root: It is known that:
[tex]\[
\sqrt[3]{2197} = 13
\][/tex]
So, the cube root of 2197 is 13.
