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It is given in the question that

Ms. Lu is adding a new room to her house. The room will be a cube with volume 4,913 cubic feet.

Let the length of the side of the puppy be x ft .

And the formula of volume of cube is

[tex]Volume = side^3[/tex]

Substituting the given values of volume, we will get

[tex]4913 = x^3

\\

x = (4913)^{1/3} = 17ft[/tex]

So the length of the sides of the  room is 17 ft .

Answer:

The length of the new room will be 17 feet.

Step-by-step explanation:

Ms. Lu is adding a new room to her house. The room will be a cube with volume 4,913 cubic feet.

The volume of cube is given as: [tex]a^{3}[/tex] where a is the edge measurement. Here, volume is given as 4913 cubic feet.

So,

[tex]a^{3}=4913[/tex]

[tex]a=\sqrt[3]{4913}[/tex]

a = 17

Hence, the length of the new room will be 17 feet.