To find the volume of a rectangular prism, you use the formula:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
For the original rectangular prism with sides 6 cm, 5 cm, and 4 cm:
\[ \text{Volume} = 6 , \text{cm} \times 5 , \text{cm} \times 4 , \text{cm} = 120 , \text{cm}^3 \]
Since the new rectangular prism is similar to the original prism and has a scale factor of 12, we can find its volume using the scale factor cubed. The volume of similar shapes changes with the cube of the scale factor:
\[ \text{Volume of new prism} = \text{Volume of original prism} \times (\text{scale factor})^3 \]
Calculating the new volume:
\[ \text{Volume of new prism} = 120 , \text{cm}^3 \times (12)^3 \]
Calculating \( (12)^3 \):
\[ (12)^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728 \]
Now, calculating the new volume:
\[ \text{Volume of new prism} = 120 , \text{cm}^3 \times 1728 = 207360 , \text{cm}^3 \]
Therefore, the volume of the new rectangular prism is \( 207360 , \text{cm}^3 \).
However, if your responses only include the following values:
- 15 cm³
- 60 cm³
- 30 cm³
- 120 cm³
Then none of those options are correct. The correct volume considering a scale factor of 12 with the given dimensions is \( 207360 , \text{cm}^3 \).
1 answer