Question

a rectangular box has its length and width doubled and its height tripled. the volume of the new box will be a. 12 times as large b. 7 times as large c. 6 times as large d. 5 times as large e. 4 times as large

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - box is $V = l\times w\times h$, where $l$ is length, $w$ is width, and $h$ is height.

Step2: Find new dimensions

The new length is $l_{new}=2l$, the new width is $w_{new}=2w$, and the new height is $h_{new}=3h$.

Step3: Calculate new volume

The new volume $V_{new}=l_{new}\times w_{new}\times h_{new}=(2l)\times(2w)\times(3h)$.
Using the associative and commutative properties of multiplication, $V_{new}=2\times2\times3\times l\times w\times h = 12lwh$.
Since the original volume $V = lwh$, the new volume is 12 times the original volume.

Answer:

A. 12 times as large