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

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 2

wrong

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!