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 find the volume of the outer box, the volume of the inner box, and then calculate the cost of the wood required to make the box.

### Step 1: Calculate the volume of the outer 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:
\[ \text{Volume} = L \times B \times H \]

Substituting the values:
\[ \text{Volume of outer box} = 22 \times 15 \times 10 \]
\[ = 3300 \, \text{cm}^3 \]

### Step 2: Calculate the inner dimensions of the box
The thickness of the wood is given as 1 cm. Therefore, we need to subtract twice the thickness from each dimension to find the inner dimensions:
- Inner Length = Outer Length - 2 × Thickness = 22 - 2 × 1 = 20 cm
- Inner Breadth = Outer Breadth - 2 × Thickness = 15 - 2 × 1 = 13 cm
- Inner Height = Outer Height - 2 × Thickness = 10 - 2 × 1 = 8 cm

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

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

### Step 5: Calculate the cost of the wood
The cost of wood is given as Rs. 1.50 per cm³. Therefore, the total cost can be calculated as:
\[ \text{Cost} = \text{Volume of wood} \times \text{Cost per cm}^3 \]
\[ = 1220 \times 1.50 \]
\[ = 1830 \, \text{Rs} \]

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

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