Internal length, breadth and depth of a rectangular box is 8 cm, 4 cm and 5 cm, respectively. How many such boxes are needed to pack 48000 cu cm?

Options

A. 250
B. 275
C. 300
D. 325

Answer

To solve the problem step by step, we need to determine the volume of one rectangular box and then find out how many such boxes are required to pack a total volume of 48,000 cubic centimeters.

### Step 1: Calculate the Volume of One Box
The formula for the volume \( V \) of a rectangular box is given by:
\[ V = \text{length} \times \text{breadth} \times \text{depth} \]
Given:
- Length = 8 cm
- Breadth = 4 cm
- Depth = 5 cm

Substituting the values:
\[ V = 8 \, \text{cm} \times 4 \, \text{cm} \times 5 \, \text{cm} \]
Calculating:
\[ V = 32 \, \text{cm}^2 \times 5 \, \text{cm} = 160 \, \text{cm}^3 \]

### Step 2: Determine the Number of Boxes Needed
Now that we have the volume of one box, we need to find out how many such boxes are required to pack a total volume of 48,000 cubic centimeters.

The number of boxes \( N \) can be calculated using the formula:
\[ N = \frac{\text{Total Volume}}{\text{Volume of One Box}} \]
Substituting the values:
\[ N = \frac{48000 \, \text{cm}^3}{160 \, \text{cm}^3} \]

### Step 3: Perform the Division
Calculating the division:
\[ N = 48000 \div 160 \]
To simplify, we can cancel out the zeros:
\[ N = \frac{480}{16} = 30 \]

### Step 4: Final Calculation
Now, multiplying by 10 (since we canceled two zeros):
\[ N = 300 \]

Thus, the number of boxes needed to pack 48,000 cubic centimeters is **300**.

### Summary
The final answer is:
\[ \text{Number of boxes needed} = 300 \]