Question
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)
6 m3
1,536 m3
384 m3
96 m3
6 m3
1,536 m3
384 m3
96 m3
Answers
GPT-4o mini
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**.
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**.