To find the volume of a cube given its surface area, follow these steps:
1. Understand the relationship between surface area and side length:
- The formula for the surface area [tex]\( A \)[/tex] of a cube with side length [tex]\( s \)[/tex] is:
[tex]\[
A = 6s^2
\][/tex]
- Here, the given surface area [tex]\( A \)[/tex] is 600 square meters.
2. Solve for the side length [tex]\( s \)[/tex]:
- Rearrange the surface area formula to solve for [tex]\( s \)[/tex]:
[tex]\[
s^2 = \frac{A}{6}
\][/tex]
- Substitute the given surface area into the equation:
[tex]\[
s^2 = \frac{600}{6} = 100
\][/tex]
- Take the square root of both sides to find [tex]\( s \)[/tex]:
[tex]\[
s = \sqrt{100} = 10 \text{ meters}
\][/tex]
3. Use the side length to find the volume:
- The formula for the volume [tex]\( V \)[/tex] of a cube with side length [tex]\( s \)[/tex] is:
[tex]\[
V = s^3
\][/tex]
- Substitute the side length [tex]\( s \)[/tex] into the volume formula:
[tex]\[
V = 10^3 = 1000 \text{ cubic meters}
\][/tex]
Therefore, the volume of the cube is [tex]\( \boxed{1000 \text{ m}^3} \)[/tex].
