A rectangular block of wood has dimensions 24 cm by 9 cm by 7 cm. It is cut into bricks. Each brick is a cube of side 3 cm. Find the largest number of bricks that can be cut from the block.

Options

A. 48
B. 56
C. 49
D. 52

Answer

To find the largest number of bricks that can be cut from a rectangular block of wood with dimensions 24 cm by 9 cm by 7 cm, where each brick is a cube of side 3 cm, we will follow these steps:

### Step 1: Calculate the volume of the rectangular block
The volume \( V \) of a rectangular block is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Substituting the given dimensions:
\[ V = 24 \, \text{cm} \times 9 \, \text{cm} \times 7 \, \text{cm} \]

### Step 2: Calculate the volume of one brick
The volume \( V_b \) of a cube is given by the formula:
\[ V_b = \text{side}^3 \]
For a cube with side 3 cm:
\[ V_b = 3 \, \text{cm} \times 3 \, \text{cm} \times 3 \, \text{cm} = 27 \, \text{cm}^3 \]

### Step 3: Calculate the total volume of the block
Now, we calculate the volume of the rectangular block:
\[ V = 24 \times 9 \times 7 = 1512 \, \text{cm}^3 \]

### Step 4: Determine how many bricks can be cut from the block
To find out how many bricks can be cut from the block, we divide the total volume of the block by the volume of one brick:
\[ \text{Number of bricks} = \frac{V}{V_b} = \frac{1512 \, \text{cm}^3}{27 \, \text{cm}^3} \]

### Step 5: Perform the division
Calculating the division:
\[ \text{Number of bricks} = \frac{1512}{27} = 56 \]

### Conclusion
The largest number of bricks that can be cut from the block is **56**.

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