Select the correct answerA cube has a total surface area of 864 cm². Find the length of one edge of the cube.Options18 cm16 cm12 cm14 cm

1. Break Down the Problem

We need to find the length of one edge of a cube, given its total surface area. The formula for the total surface area $A$ of a cube is given by: $A = 6s^2$ where $s$ is the length of one edge of the cube.

2. Relevant Concepts

Using the formula for the total surface area, we can rearrange it to solve for the edge length $s$: $s^2 = \frac{A}{6}$ Thus, we will need to substitute the given surface area into this formula.

3. Analysis and Detail

Given that the total surface area $A = 864 \, \text{cm}^2$: $s^2 = \frac{864}{6}$ Calculating this gives: $s^2 = 144$ Now, we take the square root of both sides to find $s$: $s = \sqrt{144} = 12 \, \text{cm}$

4. Verify and Summarize

The calculation indicates that the length of one edge of the cube is $12 \, \text{cm}$. To verify, we can check by substituting back into the surface area formula: $A = 6s^2 = 6 \times (12)^2 = 6 \times 144 = 864 \, \text{cm}^2$ This confirms our calculations are correct.

Final Answer

The length of one edge of the cube is 12 cm.