Calculate Sand Height in a 64 cm³ Cube: Volume to Height Conversion

Below is a cube with a volume equal to 64 cm3.

If we pour 32 cc of sand into the cube, how high will the sand reach?

Video Solution

Solution Steps

00:00 What height will the sand reach?

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

00:07 We'll take the cube root

00:13 This is the edge length of the cube

00:16 The height is the edge of the cube

00:20 We'll calculate the volume ratio between the sand and the cube

00:25 This is the volume ratio

00:30 We'll multiply this ratio by height to find the sand height

00:33 We'll substitute the height value we found and solve to find the sand height

00:38 And this is the solution to the question

Step-by-Step Solution

To solve this problem, follow these steps:

Step 1: Calculate the side length of the cube.
- The volume of the cube is $64 \, \text{cm}^3$ . Using the formula for the volume of a cube, $s^3 = 64$ .
- Find $s$ : $s = \sqrt[3]{64} = 4 \, \text{cm}$ .
Step 2: Determine the base area of the cube.
- The base of the cube is a square with side length $4 \, \text{cm}$ .
- The area, $A_{\text{base}}$ , is $4 \, \text{cm} \times 4 \, \text{cm} = 16 \, \text{cm}^2$ .
Step 3: Calculate the height the sand will reach.
- We have $32 \, \text{cm}^3$ of sand. Use the volume formula for height: $32 = 16 \times h$ .
- Solve for $h$ : $h = \frac{32}{16} = 2 \, \text{cm}$ .

Therefore, the sand will reach a height of $2 \, \text{cm}$ in the cube.