Question

a cubic box is 12 inches on each side. its height is tripled to create a new box. how does the volume of the new box compare to the volume of the original box? the volume of the new box doubles the volume is three times as large the volume is nine times as large

Explanation:

Step1: Recall the volume formula for a rectangular box

The volume \( V \) of a rectangular box is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. For the original cubic box, \( l = w = h = 12 \) inches, so the original volume \( V_{original}=12\times12\times12 \).

Step2: Determine the dimensions of the new box

The height is tripled, so the new height \( h_{new}=3\times12 \), while the length \( l_{new}=12 \) and width \( w_{new}=12 \) remain the same (since only height is changed).

Step3: Calculate the new volume

The new volume \( V_{new}=l_{new}\times w_{new}\times h_{new}=12\times12\times(3\times12) \). We can factor out the original volume: \( V_{new}=3\times(12\times12\times12)=3\times V_{original} \). So the new volume is three times the original volume.

Answer:

The volume is three times as large (the option with this text, e.g., if it's option 2, then "2. The volume is three times as large")