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A rectangular prism measures 3 meters in width, 4 meters in length, and 2 meters in height.

Determine the volume of the rectangular prism if it were dilated using a scale factor of 4.

(1 point)
Responses

1,536 m3
1,536 m cubed

6 m3
6 m cubed

96 m3
96 m cubed

384 m3
384 m cubed
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1 answer

To find the volume of a rectangular prism, the formula is given by:

\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

For the original dimensions of the prism:

  • Width = 3 meters
  • Length = 4 meters
  • Height = 2 meters

Calculating the original volume:

\[ \text{Volume} = 3 , \text{m} \times 4 , \text{m} \times 2 , \text{m} = 24 , \text{m}^3 \]

Now, if the prism is dilated using a scale factor of 4, each dimension is multiplied by this scale factor:

  • New Width = \( 3 , \text{m} \times 4 = 12 , \text{m} \)
  • New Length = \( 4 , \text{m} \times 4 = 16 , \text{m} \)
  • New Height = \( 2 , \text{m} \times 4 = 8 , \text{m} \)

Now, we calculate the new volume using the new dimensions:

\[ \text{New Volume} = 12 , \text{m} \times 16 , \text{m} \times 8 , \text{m} \]

First, calculate the product of the width and length:

\[ 12 \times 16 = 192 \]

Now multiply this result by the height:

\[ 192 \times 8 = 1536 , \text{m}^3 \]

Thus, the volume of the rectangular prism after dilation is:

1,536 m³