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

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.