Certainly! Let's solve this step by step.
1. Understand the problem:
We are given the total surface area of a cube and we need to find the length of one edge of the cube.
2. Formula for the surface area of a cube:
The surface area [tex]\( S \)[/tex] of a cube is given by:
[tex]\[
S = 6a^2
\][/tex]
where [tex]\( a \)[/tex] is the length of one edge of the cube.
3. Set up the equation:
We know the total surface area:
[tex]\[
6a^2 = 150 \text{ cm}^2
\][/tex]
4. Solve for [tex]\( a^2 \)[/tex]:
Divide both sides of the equation by 6:
[tex]\[
a^2 = \frac{150}{6}
\][/tex]
Simplifying the right-hand side:
[tex]\[
a^2 = 25 \text{ cm}^2
\][/tex]
5. Solve for [tex]\( a \)[/tex]:
To find [tex]\( a \)[/tex], take the square root of both sides:
[tex]\[
a = \sqrt{25}
\][/tex]
Therefore:
[tex]\[
a = 5 \text{ cm}
\][/tex]
6. Conclusion:
The length of one edge of the cube is [tex]\( 5 \text{ cm} \)[/tex].
