To find the length of a side of the small cubes, we need to follow these steps:
-
Determine the volume of one small cube: Since there are 24 small cubes in total and the total volume of the shape is 600 cm³, we can find the volume of one small cube by dividing the total volume by the number of cubes:
\[ \text{Volume of one cube} = \frac{\text{Total Volume}}{\text{Number of cubes}} = \frac{600 , \text{cm}^3}{24} = 25 , \text{cm}^3 \]
-
Calculate the length of a side of one cube: 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. We can take the cube root of the volume of one small cube to find \( s \):
\[ s = \sqrt[3]{25 , \text{cm}^3} \]
-
Convert the result to a numerical value:
\[ s \approx 2.924 \text{ cm} \]
Thus, the length of a side of the small cubes is approximately \( 2.92 , \text{cm} \) (rounded to two decimal places).