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?
81.84 cubic centimeters
105.84 cubic centimeters
198.264 cubic centimeters
222.264 cubic centimeters

Answer 1

The answer is letter C) 198.264 cubic centimeters

Answer 2

Answer: $198.264\text{ cubic centimeters}$

Step-by-step explanation:

Let l, w, h are be the dimensions of the smaller box such that the volume of the box is

$\text{Volume}=lwh=24$

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

Now, the volume of the larger packing box will be

$\text{Volume}\\\\=2.1l\times2.1w\times2.1w\\\\=9.261lwh\\\\9.261(24)\\\\=222.264\text{ cubic centimeters}$

Hence, the volume of the tissue paper in the packaging box= $222.264-24=198.264\text{ cubic centimeters}$