The internal length, breadth and height of a rectangular box A is 20 cm, 30 cm and 40 cm respectively and that of box B is 2 cm, 3 cm and 4 cm respectively. The volume of box A is how many times the volume of box B?

Options

A. 1000
B. 1500
C. 1200
D. 2000

Answer

To find out how many times the volume of box A is compared to the volume of box B, we will follow these steps:

### Step 1: Calculate the Volume of Box A
The formula for the volume \( V \) of a rectangular box is given by:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
For box A, the dimensions are:
- Length = 20 cm
- Breadth = 30 cm
- Height = 40 cm

Now, substituting these values into the formula:
\[ V_A = 20 \, \text{cm} \times 30 \, \text{cm} \times 40 \, \text{cm} \]
Calculating this:
\[ V_A = 20 \times 30 = 600 \, \text{cm}^2 \]
\[ V_A = 600 \times 40 = 24000 \, \text{cm}^3 \]

### Step 2: Calculate the Volume of Box B
For box B, the dimensions are:
- Length = 2 cm
- Breadth = 3 cm
- Height = 4 cm

Using the same formula:
\[ V_B = 2 \, \text{cm} \times 3 \, \text{cm} \times 4 \, \text{cm} \]
Calculating this:
\[ V_B = 2 \times 3 = 6 \, \text{cm}^2 \]
\[ V_B = 6 \times 4 = 24 \, \text{cm}^3 \]

### Step 3: Find the Ratio of the Volumes
Now, we need to find how many times the volume of box A is compared to the volume of box B:
\[ \text{Ratio} = \frac{V_A}{V_B} = \frac{24000 \, \text{cm}^3}{24 \, \text{cm}^3} \]
Calculating this:
\[ \text{Ratio} = 1000 \]

### Conclusion
The volume of box A is 1000 times the volume of box B.