Question

a clothing company wants to ship more items per box. the length, width, and height of the new boxes are all twice as long as those of the old boxes. how does the volume of a new box compare to the volume of an old box? a. the volume of the new box is 2 times the volume of the old box. b. the volume of the new box is 4 times the volume of the old box. c. the volume of the new box is 6 times the volume of the old box. d. the volume of the new box is 8 times the volume of the old box.

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. Let the length, width and height of the old box be $l_1$, $w_1$ and $h_1$ respectively, so the volume of the old box $V_1=l_1\times w_1\times h_1$.

Step2: Find dimensions of new box

The length, width and height of the new box are $l_2 = 2l_1$, $w_2 = 2w_1$ and $h_2 = 2h_1$ respectively.

Step3: Calculate volume of new box

The volume of the new box $V_2=l_2\times w_2\times h_2=(2l_1)\times(2w_1)\times(2h_1)=8l_1w_1h_1$.

Step4: Compare volumes

Since $V_1 = l_1w_1h_1$ and $V_2 = 8l_1w_1h_1$, the volume of the new box is 8 times the volume of the old box.

Answer:

D. The volume of the new box is 8 times the volume of the old box.