Question

Find the volume of a rectangular prism with a length of 8 cm, a width of 5 cm, and a height of 3 cm, and compare it to the volume of a cube with a side length of 6 cm.

Answer 1

To find the volume of the rectangular prism, we can use the formula:

\[
\text{Volume of a rectangular prism} = \text{length} \times \text{width} \times \text{height}
\]

Given:
- Length = 8 cm
- Width = 5 cm
- Height = 3 cm

Substituting in the values:

\[
\text{Volume of the prism} = 8 \, \text{cm} \times 5 \, \text{cm} \times 3 \, \text{cm} = 120 \, \text{cm}^3
\]

Next, we find the volume of the cube using the formula:

\[
\text{Volume of a cube} = \text{side}^3
\]

Given the side length of the cube is 6 cm:

\[
\text{Volume of the cube} = 6 \, \text{cm} \times 6 \, \text{cm} \times 6 \, \text{cm} = 216 \, \text{cm}^3
\]

Now, we can compare the volumes:

- Volume of the rectangular prism = 120 cm³
- Volume of the cube = 216 cm³

To compare these volumes further, we can see how many times the volume of the prism fits into the volume of the cube:

\[
\frac{\text{Volume of the cube}}{\text{Volume of the prism}} = \frac{216\, \text{cm}^3}{120\, \text{cm}^3} = 1.8
\]

Thus, the cube is approximately 1.8 times the volume of the rectangular prism.

In summary:
- Volume of the rectangular prism: \(120 \, \text{cm}^3\)
- Volume of the cube: \(216 \, \text{cm}^3\)
- The cube's volume is 1.8 times that of the rectangular prism.