Box A has a volume of 24 cubic meters. Box B is similar to Box A. To create Box B, Box A's dimensions were multiplied by 4. What is the volume of Box B? (1 point)

Question

6 m3

1,536 m3

384 m3

96 m3

Answer 1

To find the volume of Box B, we need to understand how the volume of a similar shape changes when the dimensions are scaled.

If the dimensions of Box A are multiplied by a factor of 4, the volume will increase by the cube of that factor. The formula for the new volume \( V' \) when the dimensions are scaled by a factor \( k \) is:

\[ V' = k^3 \times V \]

Here, \( V \) is the original volume and \( k \) is the scaling factor (in this case, \( k = 4 \)). The original volume of Box A is 24 cubic meters.

Now we calculate:

\[ V' = 4^3 \times 24 \] \[ V' = 64 \times 24 \] \[ V' = 1536 \text{ m}^3 \]

Therefore, the volume of Box B is 1,536 m³.