The outer dimensions of a closed wooden box are 22 cm, 15 cm and 10 cm. Thickness of the wood is 1 cm. Find the cost of wood required to make the box if `1 cm^(3)` of wood costs Rs. 1.50.

Answer

To solve the problem step by step, we will calculate the volume of the wood used to make the box and then find the cost based on the volume.

### Step 1: Calculate the outer volume of the box
The outer dimensions of the box are given as:
- Length (L) = 22 cm
- Breadth (B) = 15 cm
- Height (H) = 10 cm

The formula for the volume of a rectangular box is:
\[ \text{Volume} = L \times B \times H \]

Calculating the outer volume:
\[ \text{Outer Volume} = 22 \times 15 \times 10 \]
\[ \text{Outer Volume} = 3300 \, \text{cm}^3 \]

### Step 2: Calculate the inner dimensions of the box
The thickness of the wood is given as 1 cm. Therefore, we need to subtract 2 cm from each dimension (1 cm from each side).

- Inner Length = \( 22 - 2 = 20 \, \text{cm} \)
- Inner Breadth = \( 15 - 2 = 13 \, \text{cm} \)
- Inner Height = \( 10 - 2 = 8 \, \text{cm} \)

### Step 3: Calculate the inner volume of the box
Using the inner dimensions, we calculate the inner volume:
\[ \text{Inner Volume} = \text{Inner Length} \times \text{Inner Breadth} \times \text{Inner Height} \]
\[ \text{Inner Volume} = 20 \times 13 \times 8 \]
\[ \text{Inner Volume} = 2080 \, \text{cm}^3 \]

### Step 4: Calculate the volume of wood used
The volume of wood used to make the box is the difference between the outer volume and the inner volume:
\[ \text{Volume of Wood} = \text{Outer Volume} - \text{Inner Volume} \]
\[ \text{Volume of Wood} = 3300 - 2080 \]
\[ \text{Volume of Wood} = 1220 \, \text{cm}^3 \]

### Step 5: Calculate the cost of the wood
The cost of wood per cubic centimeter is given as Rs. 1.50. Therefore, the total cost can be calculated as:
\[ \text{Cost} = \text{Volume of Wood} \times \text{Cost per cm}^3 \]
\[ \text{Cost} = 1220 \times 1.50 \]
\[ \text{Cost} = 1830 \, \text{Rs} \]

### Final Answer
The cost of wood required to make the box is Rs. 1830.

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