Similar Figures and Volume Practice Complete this assessment to review what you’ve learned. It will not count toward your grade. 4 of 54 of 5 Items Question Use the image to answer the question. If the rectangular prism is dilated using a scale factor of 12 , what would be the volume of the dilated rectangular prism? (1 point) m3 Remaining Attempts : 3 Skip to navigation page 13 of 14 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To find the volume of the dilated rectangular prism, we first need to understand how dilation affects the volume of a 3D figure.

The volume \( V \) of a rectangular prism can be found using the formula: \[ V = l \times w \times h \] where \( l \) is the length, \( w \) is the width, and \( h \) is the height of the prism.

When a figure is dilated by a scale factor \( k \), the new volume \( V' \) can be calculated using the formula: \[ V' = k^3 \times V \] where \( k \) is the scale factor and \( V \) is the original volume.

In this case, the scale factor \( k \) is given as \( 12 \).

Thus, the volume of the dilated rectangular prism will be: \[ V' = 12^3 \times V \] Calculating \( 12^3 \): \[ 12^3 = 12 \times 12 \times 12 = 1728 \]

So, the volume of the dilated rectangular prism is: \[ V' = 1728 \times V \]

Therefore, if you know the original volume \( V \) of the rectangular prism, multiply it by 1728 to find the volume of the dilated prism.

If the original volume \( V \) is provided, substituting that value will give you the specific volume of the dilated rectangular prism. If you need further assistance or the original volume, please provide the original dimensions, and I can help you calculate the actual volume.