Answer :
To find the length of the new room that Ms. Lu is adding, we'll need to determine the side length of a cube that has a volume of 4,913 cubic feet.
The volume [tex]\( V \)[/tex] of a cube is given by the formula:
[tex]\[
V = s^3
\][/tex]
where [tex]\( s \)[/tex] is the side length of the cube.
Given the volume [tex]\( V = 4,913 \)[/tex] cubic feet, we need to solve for [tex]\( s \)[/tex].
1. Set up the equation:
[tex]\[
4913 = s^3
\][/tex]
2. Solve for [tex]\( s \)[/tex]: To find [tex]\( s \)[/tex], we need to take the cube root of both sides of the equation.
[tex]\[
s = \sqrt[3]{4913}
\][/tex]
3. Compute the cube root:
Evaluating the cube root of 4913, we find:
[tex]\[
s = 16.999999999999996
\][/tex]
So, the side length of the new room is approximately [tex]\( 17 \)[/tex] feet if rounded to the nearest whole number, but for the most precise value, it is [tex]\( 16.999999999999996 \)[/tex] feet.
The volume [tex]\( V \)[/tex] of a cube is given by the formula:
[tex]\[
V = s^3
\][/tex]
where [tex]\( s \)[/tex] is the side length of the cube.
Given the volume [tex]\( V = 4,913 \)[/tex] cubic feet, we need to solve for [tex]\( s \)[/tex].
1. Set up the equation:
[tex]\[
4913 = s^3
\][/tex]
2. Solve for [tex]\( s \)[/tex]: To find [tex]\( s \)[/tex], we need to take the cube root of both sides of the equation.
[tex]\[
s = \sqrt[3]{4913}
\][/tex]
3. Compute the cube root:
Evaluating the cube root of 4913, we find:
[tex]\[
s = 16.999999999999996
\][/tex]
So, the side length of the new room is approximately [tex]\( 17 \)[/tex] feet if rounded to the nearest whole number, but for the most precise value, it is [tex]\( 16.999999999999996 \)[/tex] feet.
