Answer:
![493.039 \;in^3](https://img.qammunity.org/2023/formulas/mathematics/college/hutjou4o23thf0boxwgkd0ce3vuifpw9ol.png)
Explanation:
If each side of the cube is
then the volume of the cube is given by
![a^3](https://img.qammunity.org/2023/formulas/mathematics/high-school/acsblf5gg27imyrj9qgiy3g29ok0onijkg.png)
If Volume is
then each side
![a = \sqrt[3]{V}](https://img.qammunity.org/2023/formulas/mathematics/college/cie0ljnwu56dgs24lbk39pfc0541a057ev.png)
Here we are given the volume of the smaller cube as
![85\; in^3](https://img.qammunity.org/2023/formulas/mathematics/college/hjk9pyek6n51i33d7rk70j767w5ibduz7h.png)
So each side of this cube =
![\sqrt[3]{85} = 4.396 \approx 4.4 \;in](https://img.qammunity.org/2023/formulas/mathematics/college/oovbjxwriapa6mblxt6co8l4npd5t3aj2i.png)
and each side of the larger cube
![= 4.4 + 3.5 = 7.9\;in](https://img.qammunity.org/2023/formulas/mathematics/college/21aot391co5qdqtkvdm31gmamo6s635kkq.png)
Volume of larger cube
![= 7.9^3 = 493.039 \; in^3](https://img.qammunity.org/2023/formulas/mathematics/college/tdbatbx9xx989qnv3i75ukabhes8wzxrni.png)