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 space filled with tissue paper in the packaging box? 81.84 cubic centimeters 105.84 cubic centimeters 198.264 cubic centimeters 222.264 cubic centimeters

Explanation:

Step1: Recall volume scale factor

For similar solids, if the linear scale factor is \( k \), the volume scale factor is \( k^3 \). Here, \( k = 2.1 \), so volume scale factor is \( 2.1^3 \).
\( 2.1^3=2.1\times2.1\times2.1 = 9.261 \)

Step2: Calculate volume of larger box

Volume of smaller box is \( 24 \, \text{cm}^3 \). Volume of larger box \( V_{large}=24\times9.261 \)
\( 24\times9.261 = 222.264 \, \text{cm}^3 \)

Step3: Find volume of tissue paper

Volume of tissue paper \( = V_{large}-V_{small}=222.264 - 24 \)
\( 222.264-24 = 198.264 \, \text{cm}^3 \)

Answer:

198.264 cubic centimeters