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A cube has a surface area of 600 square meters. What is its volume?

A. [tex]\(300 \, \text{m}^3\)[/tex]

B. [tex]\(1000 \, \text{m}^3\)[/tex]

C. [tex]\(600 \, \text{m}^3\)[/tex]

D. [tex]\(100 \, \text{m}^3\)[/tex]

Sagot :

GinnyAnswer
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].
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