To determine the length of the side of a cube when given the total surface area, you can follow these steps:
1. Understand the Formula for the Surface Area of a Cube:
The total surface area [tex]\( A \)[/tex] of a cube can be calculated with the formula:
[tex]\[
A = 6 \times a^2
\][/tex]
where [tex]\( a \)[/tex] is the length of a side of the cube.
2. Substitute the Given Value:
In this problem, the total surface area [tex]\( A \)[/tex] is given as [tex]\( 2400 \, \text{cm}^2 \)[/tex]. So, we have:
[tex]\[
2400 = 6 \times a^2
\][/tex]
3. Solve for [tex]\( a^2 \)[/tex]:
To isolate [tex]\( a^2 \)[/tex], divide both sides of the equation by 6:
[tex]\[
a^2 = \frac{2400}{6}
\][/tex]
4. Perform the Division:
Calculate the right-hand side:
[tex]\[
a^2 = 400
\][/tex]
5. Solve for [tex]\( a \)[/tex]:
To find [tex]\( a \)[/tex], take the square root of both sides of the equation:
[tex]\[
a = \sqrt{400}
\][/tex]
6. Calculate the Square Root:
[tex]\[
a = 20
\][/tex]
Thus, the length of a side of the cube is [tex]\( 20 \, \text{cm} \)[/tex].
