How many cubes of volume 216 `cm^(3)` can be obtained from a cube whose side is 36 cm ?

Options

A. 216
B. 125
C. 729
D. 343

Answer

To solve the problem of how many cubes of volume 216 cm³ can be obtained from a cube whose side is 36 cm, we will follow these steps:

### Step-by-Step Solution:

1. **Calculate the volume of the larger cube:**
The volume \( V \) of a cube is given by the formula:
\[ V = \text{side}^3 \]
For the larger cube with a side of 36 cm:
\[ V = 36^3 = 36 \times 36 \times 36 \]

2. **Calculate \( 36^3 \):**
First, calculate \( 36 \times 36 \):
\[ 36 \times 36 = 1296 \]
Now multiply this result by 36:
\[ 1296 \times 36 = 46656 \text{ cm}^3 \]
So, the volume of the larger cube is \( 46656 \text{ cm}^3 \).

3. **Volume of the smaller cube:**
The volume of the smaller cube is given as \( 216 \text{ cm}^3 \).

4. **Calculate the number of smaller cubes that can fit into the larger cube:**
To find the number of smaller cubes that can fit into the larger cube, divide the volume of the larger cube by the volume of the smaller cube:
\[ \text{Number of smaller cubes} = \frac{\text{Volume of larger cube}}{\text{Volume of smaller cube}} = \frac{46656}{216} \]

5. **Perform the division:**
Now, calculate \( \frac{46656}{216} \):
\[ \frac{46656}{216} = 216 \]

Thus, the number of cubes of volume 216 cm³ that can be obtained from a cube whose side is 36 cm is **216**.