Calculate Water Height: Finding Level in 125 cm³ Cube with 75 cm³ Water

To solve this problem, we'll follow these steps:

• Step 1: Calculate the side length of the cube.
• Step 2: Find the base area of the cube.
• Step 3: Determine the height the water reaches based on its volume.

Now, let's work through each step:

Step 1: The volume of the cube is $125 \, \text{cm}^3$. Since the volume of a cube is given by $s^3$, we have:

$s^3 = 125$

Taking the cube root of both sides gives:

$s = \sqrt[3]{125} = 5 \, \text{cm}$

Step 2: The base area of the cube is $s^2$, which is:

$(5 \, \text{cm})^2 = 25 \, \text{cm}^2$

Step 3: The volume of water is $75 \, \text{cm}^3$, and we need to find the height $h$ it reaches in the cube:

$75 = 25 \times h$

Solving for $h$:

$h = \frac{75}{25} = 3 \, \text{cm}$

Therefore, the height to which the water will reach is $3 \, \text{cm}$.