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To find the volume of a cube given its total surface area, you can follow these steps:
1. The formula for the total surface area ( A ) of a cube is:
[
A = 6s^2
]
where ( s ) is the length of a side of the cube.
2. Given that the total surface area ( A = 24 ) sq. units, we can set up the equation:
[
6s^2 = 24
]
3. Now, solve for ( s^2 ):
[
s^2 = frac{24}{6} = 4
]
4. Taking the square root of both sides, we get:
[
s = sqrt{4} = 2 text{ units}
]
5. The volume ( V ) of a cube is given by the formula:
[
V = s^3
]
6. Substituting the value of ( s ):
[
V = 2^3 = 8 text{ cubic units}
]
Therefore, the volume of the cube is ( 8 ) cubic units.