A rectangular solid of metal has dimensions 50 cm , 64 cm and 72 cm . It is melted and recasted into indentical cubes each with edge 4 cm , find the number of cubes formed

Answer

To solve the problem step by step, we need to find the volume of the rectangular solid and then determine how many identical cubes can be formed from that volume.

### Step 1: Calculate the Volume of the Rectangular Solid
The volume \( V \) of a rectangular solid can be calculated using the formula:
\[ V = \text{length} \times \text{width} \times \text{height} \]
Given the dimensions of the rectangular solid are 50 cm, 64 cm, and 72 cm, we can substitute these values into the formula.

\[ V = 50 \, \text{cm} \times 64 \, \text{cm} \times 72 \, \text{cm} \]

### Step 2: Perform the Multiplication
Now we will multiply the dimensions:

1. First, multiply 50 cm and 64 cm:
\[ 50 \times 64 = 3200 \, \text{cm}^2 \]

2. Next, multiply the result by 72 cm:
\[ 3200 \times 72 = 230400 \, \text{cm}^3 \]

So, the volume of the rectangular solid is:
\[ V = 230400 \, \text{cm}^3 \]

### Step 3: Calculate the Volume of One Cube
The volume \( V_c \) of a cube can be calculated using the formula:
\[ V_c = \text{edge}^3 \]
Given that the edge of each cube is 4 cm, we can substitute this value into the formula.

\[ V_c = 4 \, \text{cm} \times 4 \, \text{cm} \times 4 \, \text{cm} = 64 \, \text{cm}^3 \]

### Step 4: Calculate the Number of Cubes
To find the number of cubes formed, we divide the volume of the rectangular solid by the volume of one cube:

\[ \text{Number of cubes} = \frac{V}{V_c} = \frac{230400 \, \text{cm}^3}{64 \, \text{cm}^3} \]

### Step 5: Perform the Division
Now we will perform the division:

\[ \text{Number of cubes} = \frac{230400}{64} = 3600 \]

### Final Answer
The number of identical cubes formed is:
\[ \text{Number of cubes} = 3600 \]

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