To find the length of a side of the small cubes, we start by determining the volume of one small cube.
Given:
- Total volume of the 3-dimensional shape = 600 cm³
- Number of small cubes = 24
We can calculate the volume of one small cube using the formula:
\[ \text{Volume of one small cube} = \frac{\text{Total volume}}{\text{Number of cubes}} = \frac{600 , \text{cm}^3}{24} \]
Calculating that gives:
\[ \text{Volume of one small cube} = 25 , \text{cm}^3 \]
Next, we know that the volume \(V\) of a cube is given by the formula:
\[ V = s^3 \]
where \(s\) is the length of a side of the cube. To find \(s\), we set the volume of one small cube equal to \(s^3\):
\[ s^3 = 25 , \text{cm}^3 \]
Now, we need to find \(s\), which involves taking the cube root of both sides:
\[ s = \sqrt[3]{25} \]
Calculating the cube root of 25:
\[ s \approx 2.924 , \text{cm} \]
Thus, the length of a side of the small cubes is approximately \(2.92 , \text{cm}\).
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