The room will be a cube with volume 4,913 cubic feet. what is tje length of the new room

Volume is equal to length×width×height and in a cube those three values are equal to each other.  that means if you call the value of length to be equal to x meters, the values for height and width would also be equal to x.
therefore x³=Volume in the case of a cube.
x³=4913 cubic meters
x=17 meters

I hope this helps.  Let me know if anything is unclear.