A metal cuboid of dimensions 49 m , 22 m , and 14 m is melted and cast into cubes such that the side of each cube is equal to the half of the height of each cuboid . The number of cubes , thus , formed is __________.

Options

A. 88
B. 44
C. 22
D. 110

Answer

To solve the problem, we will follow these steps:

### Step 1: Find the volume of the cuboid.
The formula for the volume \( V \) of a cuboid is given by:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given dimensions:
- Length = 49 m
- Breadth = 22 m
- Height = 14 m

Substituting the values:
\[ V = 49 \times 22 \times 14 \]

### Step 2: Calculate the volume of the cuboid.
Calculating the volume:
\[ V = 49 \times 22 = 1078 \]
Now, multiply by the height:
\[ V = 1078 \times 14 = 15092 \text{ m}^3 \]

### Step 3: Find the side length of the cube.
The side length of each cube is given as half of the height of the cuboid. Since the height of the cuboid is 14 m:
\[ \text{Side of cube} = \frac{14}{2} = 7 \text{ m} \]

### Step 4: Calculate the volume of one cube.
The volume \( V_c \) of a cube is given by:
\[ V_c = \text{side}^3 \]
Substituting the side length:
\[ V_c = 7^3 = 7 \times 7 \times 7 = 343 \text{ m}^3 \]

### Step 5: Calculate the number of cubes formed.
To find the number of cubes, divide the volume of the cuboid by the volume of one cube:
\[ \text{Number of cubes} = \frac{V}{V_c} = \frac{15092}{343} \]

### Step 6: Perform the division.
Calculating the number of cubes:
\[ \text{Number of cubes} = 44 \]

### Final Answer:
The number of cubes formed is **44**.

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