Question

Zoe is packaging a gift to send in the mail. A smaller gift box is placed inside a similar yet larger packaging box. The empty space inside the packaging box is filled with tissue paper to keep the gift box from moving. The dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box. The volume of the smaller box is 24 cubic centimeters.What is the volume of the tissue paper in the packaging box?

Answer 1

198.264 cubic cm is the volume of tissues in the box.

Explanation:

Let us take the dimensions of the smaller box as l, w, h (length, width, height)

Volume of the box is given as 24 cubic cm.

`l * w * h=24`

As given, the dimensions of the larger box are each 2.1 times longer than the corresponding dimensions of the smaller box.

So, the volume of the larger packing box will become:

`2.1l *2.1w*2.1h` = 9.261 lwh

Now, already we know lwh = 24

So, Volume of larger box is :

`9.261*24=222.264` cubic cm

Therefore, the volume of the tissue paper in the packaging box is :

`222.264-24=198.264` cubic cm.

Answer 2

Packing boxes are similar shapes with the coefficient of similarity k=2.1. The volumes of similar shapes are proportional with the coefficient

`K=k^3=2.1^3=9.261.`

Then

`(V_(large))/(V_(small))=K\Rightarrow V_(large)=9.261V_(small)=9.261\cdot 24=222.264\ cm^3.`

The volume of the tissue paper in the packaging box is

`V_(paper)=V_(large)-V_(small)=222.264-24=198.264\ cm^3.`

Answer:
`198.264\ cm^3.`