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.

Answer 1

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 \(2.92 \, \text{cm}\).