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

Video Solution

Solution Steps

00:00 To what height will the water reach?

00:03 We'll use the formula for volume calculation (edge cubed)

00:07 We'll extract the cube root

00:12 This is the size of edge A

00:22 The height of the cube is the edge

00:27 We'll calculate the volume ratio

00:31 This is the volume ratio

00:34 The volume ratio equals the height ratio

00:38 We'll multiply the height by the ratio to find the water height

00:42 And this is the solution to the question

Step-by-Step Solution

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

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 $3 \, \text{cm}$ .