A wooden box measures 20 cm by 12 cm by 10cm. Thickness of wood is 1 cm. Volume of wood to make the box (in cubic cm) is

Options

A. 960
B. 519
C. 2400
D. 1120

Answer

To find the volume of wood used to make the wooden box, we need to calculate the external volume of the box and the internal volume of the box, and then subtract the internal volume from the external volume.

### Step-by-Step Solution:

1. **Calculate the External Volume of the Box:**
The external dimensions of the box are given as:
- Length (L) = 20 cm
- Breadth (B) = 12 cm
- Height (H) = 10 cm

The formula for the volume of a rectangular box is:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the values:
\[ \text{External Volume} = 20 \, \text{cm} \times 12 \, \text{cm} \times 10 \, \text{cm} = 2400 \, \text{cm}^3 \]

2. **Calculate the Internal Dimensions of the Box:**
Since the thickness of the wood is 1 cm, we need to subtract 2 cm from each dimension (1 cm from each side):
- Internal Length = 20 cm - 2 cm = 18 cm
- Internal Breadth = 12 cm - 2 cm = 10 cm
- Internal Height = 10 cm - 2 cm = 8 cm

3. **Calculate the Internal Volume of the Box:**
Using the internal dimensions:
\[ \text{Internal Volume} = \text{Internal Length} \times \text{Internal Breadth} \times \text{Internal Height} \]
Substituting the values:
\[ \text{Internal Volume} = 18 \, \text{cm} \times 10 \, \text{cm} \times 8 \, \text{cm} = 1440 \, \text{cm}^3 \]

4. **Calculate the Volume of Wood Used:**
The volume of wood used to make the box is the difference between the external volume and the internal volume:
\[ \text{Volume of Wood} = \text{External Volume} - \text{Internal Volume} \]
Substituting the calculated volumes:
\[ \text{Volume of Wood} = 2400 \, \text{cm}^3 - 1440 \, \text{cm}^3 = 960 \, \text{cm}^3 \]

### Final Answer:
The volume of wood used to make the box is **960 cm³**.