It takes 125 identical wooden cubes to fill a cubical box. How many of these cubes does it take to cover the bottom of the box?
Could someone explain this one to me?
125 is a perfect cube, namely 5^3
so the box is 5 by 5 by 5
and the area of the bottom would be 25,
so it would take 25 of the cubes to fill the bottom layer.
To determine the number of cubes needed to cover the bottom of the box, we need to find the area of the bottom surface of the box first.
Since the box is cubical, each side represents a square. Let's assume that each side of the box is made up of `n` wooden cubes. Therefore, the total number of cubes used to fill the box would be `n x n x n`, which simplifies to n^3.
According to the given information, it takes 125 identical wooden cubes to fill the box, so we can set up the equation n^3 = 125.
Taking the cube root of both sides, we get n = ∛(125). The cube root of 125 is 5, so n = 5.
Now that we know each side of the box has 5 cubes, we can calculate the total number of cubes needed to cover the bottom of the box. The bottom surface area of a cube is given by one side squared, which is 5 x 5 = 25.
So, it takes 25 identical wooden cubes to cover the bottom of the box.