Sure, let's solve these problems step by step.
### (a) Finding the side length of a cubical box with volume 216 cm³
Given:
- Volume [tex]\( V \)[/tex] of the cube is 216 cm³.
The formula to find the side length [tex]\( s \)[/tex] of a cube given its volume is:
[tex]\[ V = s^3 \][/tex]
We need to solve for [tex]\( s \)[/tex]:
[tex]\[ s = \sqrt[3]{V} \][/tex]
Substitute the given volume:
[tex]\[ s = \sqrt[3]{216} \][/tex]
When you calculate the cube root of 216, you get:
[tex]\[ s \approx 6.0 \, \text{cm} \][/tex]
So, the length of each side of the cubical box is approximately 6.0 cm.
### (b) Finding the side length of a cube with volume 1,728 cm³
Given:
- Volume [tex]\( V \)[/tex] of the cube is 1,728 cm³.
Similarly, use the formula:
[tex]\[ V = s^3 \][/tex]
Solving for [tex]\( s \)[/tex]:
[tex]\[ s = \sqrt[3]{1,728} \][/tex]
Upon calculating the cube root of 1,728, you get:
[tex]\[ s \approx 12.0 \, \text{cm} \][/tex]
So, the length of each side of the cube is approximately 12.0 cm.
Thus, the solutions are:
- For part (a), the side length of the cubical box is approximately 6.0 cm.
- For part (b), the side length of the cube is approximately 12.0 cm.
