The outer dimensions of a closed box are 15 cm by 13 cm by 10 cm . Thickness of the wood is 2 cm. Find the total cost of wood required to make the box if `1 cm ^(3)` of wood costs Rs. 5.00

Options

A. Rs. 6780
B. Rs. 2020
C. Rs. 4880
D. Rs. 8210

Answer

To solve the problem, we need to find the volume of wood used to make the box. This can be done by calculating the volume of the outer box and subtracting the volume of the inner box (which is hollow).

### Step-by-step Solution:

1. **Calculate the outer volume of the box:**
The outer dimensions of the box are given as:
- Length (L) = 15 cm
- Width (W) = 13 cm
- Height (H) = 10 cm

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

Substituting the outer dimensions:
\[ \text{Outer Volume} = 15 \times 13 \times 10 = 1950 \, \text{cm}^3 \]

2. **Calculate the inner dimensions of the box:**
Since the thickness of the wood is 2 cm, we need to subtract twice the thickness from each dimension to get the inner dimensions:
- Inner Length = \(15 - 2 \times 2 = 15 - 4 = 11 \, \text{cm}\)
- Inner Width = \(13 - 2 \times 2 = 13 - 4 = 9 \, \text{cm}\)
- Inner Height = \(10 - 2 \times 2 = 10 - 4 = 6 \, \text{cm}\)

3. **Calculate the inner volume of the box:**
Using the inner dimensions:
\[ \text{Inner Volume} = 11 \times 9 \times 6 \]
\[ \text{Inner Volume} = 594 \, \text{cm}^3 \]

4. **Calculate the volume of wood used:**
The volume of wood used is the difference between the outer volume and the inner volume:
\[ \text{Volume of Wood} = \text{Outer Volume} - \text{Inner Volume} \]
\[ \text{Volume of Wood} = 1950 - 594 = 1356 \, \text{cm}^3 \]

5. **Calculate the cost of the wood:**
Given that 1 cm³ of wood costs Rs. 5.00, we can calculate the total cost:
\[ \text{Total Cost} = \text{Volume of Wood} \times \text{Cost per cm}^3 \]
\[ \text{Total Cost} = 1356 \times 5 = 6780 \, \text{Rs.} \]

### Final Answer:
The total cost of wood required to make the box is Rs. 6780.