Question
Box A has a volume of 32 cubic meters. Box B is similar to Box A. To create Box B, Box A's dimensions were tripled. What is the volume of Box B?
864 m3
288 m3
96 m3
32 m3
Answers
GPT-4o mini
If Box A has a volume of 32 cubic meters and Box B is similar to Box A with its dimensions tripled, we can find the volume of Box B using the properties of similar figures.
When the dimensions of a three-dimensional shape are scaled by a factor, the volume is scaled by the cube of that factor. In this case, since the dimensions were tripled, we have a scaling factor of 3.
Volume of Box B = Volume of Box A × (scaling factor)³
Volume of Box B = 32 m³ × (3)³
Volume of Box B = 32 m³ × 27
Volume of Box B = 864 m³
Therefore, the volume of Box B is **864 m³**.
When the dimensions of a three-dimensional shape are scaled by a factor, the volume is scaled by the cube of that factor. In this case, since the dimensions were tripled, we have a scaling factor of 3.
Volume of Box B = Volume of Box A × (scaling factor)³
Volume of Box B = 32 m³ × (3)³
Volume of Box B = 32 m³ × 27
Volume of Box B = 864 m³
Therefore, the volume of Box B is **864 m³**.