Question

ms. lu is adding a new room to her house. the room will be a cube with a volume of 4,913 cubic feet. what is the length of the new room? (simplify your answer.)

Explanation:

Step1: Recall volume formula for cube

The volume formula for a cube is $V = s^3$, where $s$ is the side - length (which is the length in this case as all sides of a cube are equal) and $V$ is the volume.

Step2: Solve for side - length

Given $V = 4913$ cubic feet. We need to find $s$ such that $s^3=4913$. So, $s=\sqrt[3]{4913}$.
Since $17\times17\times17 = 4913$ (because $17\times17 = 289$ and $289\times17=4913$), $s = 17$ feet.

Answer:

17 feet