Question

determine the volume of the figure ( L = 10 cm, W = 8 cm, H = 6 cm) if it were dilated using a scale factor of 2

Answer 1

wrong

Answer 2

To determine the volume of the figure after dilation, we can follow these steps:

1. **Calculate the volume of the original figure**. The volume \( V \) of a rectangular prism is given by the formula:
\[
V = L \times W \times H
\]
where \( L \) is the length, \( W \) is the width, and \( H \) is the height.

For the given dimensions:
\[
L = 10 \, \text{cm}, \quad W = 8 \, \text{cm}, \quad H = 6 \, \text{cm}
\]
Thus, the volume of the original figure is:
\[
V = 10 \, \text{cm} \times 8 \, \text{cm} \times 6 \, \text{cm} = 480 \, \text{cm}^3
\]

2. **Apply the scale factor for the dilation**. When a three-dimensional figure is dilated by a scale factor \( k \), the volume of the new figure is given by:
\[
V' = k^3 \times V
\]
where \( V' \) is the volume of the dilated figure and \( k \) is the scale factor.

In this case, the scale factor is \( k = 2 \). So:
\[
V' = 2^3 \times 480 \, \text{cm}^3
\]
Calculating \( 2^3 \):
\[
2^3 = 8
\]
Therefore:
\[
V' = 8 \times 480 \, \text{cm}^3 = 3840 \, \text{cm}^3
\]

The volume of the figure after dilation using a scale factor of 2 is **3840 cm³**.

Answer 3

Let’s review the calculation step-by-step to ensure accuracy and clarify any misunderstandings.

1. **Calculate the Volume of the Original Figure**:
The volume \( V \) of a rectangular prism is calculated using the formula:
\[
V = L \times W \times H
\]

Given:
- Length \( L = 10 \, \text{cm} \)
- Width \( W = 8 \, \text{cm} \)
- Height \( H = 6 \, \text{cm} \)

The original volume is:
\[
V = 10 \, \text{cm} \times 8 \, \text{cm} \times 6 \, \text{cm} = 480 \, \text{cm}^3
\]

2. **Dilation with Scale Factor**:
When a three-dimensional object is dilated by a scale factor \( k \), the new volume \( V' \) is given by:
\[
V' = k^3 \times V
\]

Here, the scale factor \( k = 2 \). Thus, we need to calculate \( k^3 \):
\[
k^3 = 2^3 = 8
\]

3. **Calculate the Volume After Dilation**:
Now we apply the scale factor to the original volume:
\[
V' = 8 \times 480 \, \text{cm}^3 = 3840 \, \text{cm}^3
\]

Therefore, the final volume after dilation of the figure with a scale factor of 2 is indeed **3840 cm³**.

If you believe there was a misunderstanding in my earlier response or if there's anything specific you'd like me to correct or clarify, please let me know!