Kyle has a large, cube-shaped eerrerium for his iguana. He wants to cover the opening with a square screenWhat are the dimensions, 5 , for the screen? \[ \begin{array}{rlr} V=s^{3} & \begin{array}{l} \text { The value of } s \text { is not } \\ 343 \end{array}=s^{3} & \begin{array}{l} \pm \sqrt{343} \text { because } \\ \sqrt{343} \end{array}=\sqrt{5^{3}} \\ 7 & =s & \begin{array}{l} (-7)^{3}=-7 \times-7 \times-7 \\ \\ 7 \end{array} \end{array} \] Each edge of the tervarium is 7 feet, so the dimensions of the screen are 7 feet by 7 feet.

Let's break down the problem step by step to find the dimensions of the screen that Kyle needs to cover the opening of his cube-shaped terrarium. 1. **Understanding the Volume of the Cube:** The volume \( V \) of a cube is given by the formula: \[ V = s^3 \] where \( s \) is the length of each edge of the cube. 2. **Given Volume:** We know that the volume is \( 343 \) cubic feet. Therefore, we can set up the equation: \[ s^3 = 343 \] 3. **Finding the Length of Each Edge:** To find \( s \), we need to take the cube root of \( 343 \): \[ s = \sqrt[3]{343} \] 4. **Calculating the Cube Root:** We can simplify \( 343 \) as follows: \[ 343 = 7^3 \] Thus, taking the cube root gives us: \[ s = 7 \text{ feet} \] 5. **Dimensions of the Screen:** Since the opening of the cube is square and each edge of the cube is \( 7 \) feet, the dimensions of the screen that Kyle needs to cover the opening are: \[ 7 \text{ feet} \times 7 \text{ feet} \] In conclusion, the dimensions of the screen are \( 7 \) feet by \( 7 \) feet.