Final answer:
The dimensions for a square screen to cover a cube-shaped terrarium with a volume of 343 cubic feet is 7 feet by 7 feet, as determined by taking the cube root of the volume.
Step-by-step explanation:
The student asked about the dimensions, s, for a square screen to cover a cube-shaped terrarium having a volume of 343 cubic feet. To find the dimensions, one must first understand that the volume (V) of a cube is equal to s cubed (s³), where s is the length of one side of the cube. Therefore, the cube root of the volume will give us the dimension of one side of the cube.
To find the dimension of the side, we calculate the cube root of 343 cubic feet, which is 7 feet. Since the terrarium is cube-shaped, all sides are equal, and thus, the dimension of the square screen needed to cover it will also be 7 feet by 7 feet.
Calculation Steps:
- Identify the volume of the cube: V = 343 ft³.
- Calculate the cube root of the volume to find the side length: s = ∛(343 ft³) = 7 ft.
- Since the screen must cover the cube, its dimensions will match the side of the cube: screen dimensions = 7 ft by 7 ft.
This process shows the direct relationship between the volume of a cube and the length of its sides, which is pivotal for understanding geometric properties in real-world applications.