The internal measurements of a box with lid are `115 xx 75 xx 35` cm3 and the wood of which it is made is 2.5 cm thick. Find the volume of wood.

Options

A. `82,125 cm^(3)`
B. `70,054 cm^(3)`
C. `78,514 cm^(3)`
D. None of these

Answer

To find the volume of wood used in the box, we will first calculate the outer dimensions of the box and then find both the inner and outer volumes. Finally, we will subtract the inner volume from the outer volume to get the volume of the wood.

### Step-by-Step Solution:

1. **Identify the Internal Dimensions:**
- The internal dimensions of the box are given as:
- Length (L) = 115 cm
- Width (W) = 75 cm
- Height (H) = 35 cm

2. **Calculate the Outer Dimensions:**
- The thickness of the wood is given as 2.5 cm. To find the outer dimensions, we need to add the thickness to both sides of each dimension.
- Outer Length (L') = Internal Length + 2 * Thickness
\[ L' = 115 + 2 \times 2.5 = 115 + 5 = 120 \text{ cm} \]
- Outer Width (W') = Internal Width + 2 * Thickness
\[ W' = 75 + 2 \times 2.5 = 75 + 5 = 80 \text{ cm} \]
- Outer Height (H') = Internal Height + 2 * Thickness
\[ H' = 35 + 2 \times 2.5 = 35 + 5 = 40 \text{ cm} \]

3. **Calculate the Inner Volume:**
- The inner volume (V_inner) can be calculated using the formula for the volume of a rectangular box:
\[ V_{inner} = L \times W \times H = 115 \times 75 \times 35 \]
- Performing the multiplication:
\[ V_{inner} = 115 \times 75 = 8625 \]
\[ V_{inner} = 8625 \times 35 = 301875 \text{ cm}^3 \]

4. **Calculate the Outer Volume:**
- The outer volume (V_outer) can also be calculated using the same formula:
\[ V_{outer} = L' \times W' \times H' = 120 \times 80 \times 40 \]
- Performing the multiplication:
\[ V_{outer} = 120 \times 80 = 9600 \]
\[ V_{outer} = 9600 \times 40 = 384000 \text{ cm}^3 \]

5. **Calculate the Volume of Wood:**
- The volume of wood (V_wood) is the difference between the outer volume and the inner volume:
\[ V_{wood} = V_{outer} - V_{inner} = 384000 - 301875 \]
- Performing the subtraction:
\[ V_{wood} = 82125 \text{ cm}^3 \]

### Final Answer:
The volume of wood used in the box is **82125 cm³**.