Question

A 3-dimensional shape consists of 24 small cubes of equal sizes. If the shape has a volume of 600〖cm〗^3, calculate the length of a side of the small cubes. (5)

Answer 1

To find the length of a side of the small cubes, we need to follow these steps:

1. **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:

\[
\text{Volume of one cube} = \frac{\text{Total Volume}}{\text{Number of cubes}} = \frac{600 \, \text{cm}^3}{24} = 25 \, \text{cm}^3
\]

2. **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 \( s \):

\[
s = \sqrt[3]{25 \, \text{cm}^3}
\]

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).