To determine whether the volume of the given cuboid is the same as that of a cube with a side length of 30 cm, follow these steps:
1. Calculate the volume of the cuboid:
The formula to find the volume of a cuboid is:
[tex]\[
\text{Volume of cuboid} = \text{length} \times \text{width} \times \text{height}
\][/tex]
Given dimensions of the cuboid are:
- Length = 50 cm
- Width = 20 cm
- Height = 24 cm
Plugging in these values:
[tex]\[
\text{Volume of cuboid} = 50 \, \text{cm} \times 20 \, \text{cm} \times 24 \, \text{cm} = 24000\, \text{cm}^3
\][/tex]
2. Calculate the volume of the cube:
The formula to find the volume of a cube is:
[tex]\[
\text{Volume of cube} = \text{side}^3
\][/tex]
Given side length of the cube is 30 cm. So:
[tex]\[
\text{Volume of cube} = 30\, \text{cm} \times 30\, \text{cm} \times 30\, \text{cm} = 27000\, \text{cm}^3
\][/tex]
3. Compare the volumes:
- Volume of the cuboid = 24000 cm³
- Volume of the cube = 27000 cm³
Comparing the two volumes, we see that:
- [tex]\(24000\, \text{cm}^3 \neq 27000\, \text{cm}^3\)[/tex]
Therefore, the volume of the cuboid is not the same as the volume of the cube. The cuboid has a smaller volume compared to the cube.
