A wooden box with dimensions `36cmxx24cmxx12 cm` is 2cm thick. Find the weight of the wood if density of the wood is 100`gm//m^(3)`

Answer

To find the weight of the wood used in a wooden box with given dimensions and thickness, follow these steps:

### Step 1: Determine the outer dimensions of the box
The outer dimensions of the box are given as:
- Length (L) = 36 cm
- Breadth (B) = 24 cm
- Height (H) = 12 cm

### Step 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 find the inner dimensions:
- Inner Length = 36 cm - 2*2 cm = 36 cm - 4 cm = 32 cm
- Inner Breadth = 24 cm - 2*2 cm = 24 cm - 4 cm = 20 cm
- Inner Height = 12 cm - 2*2 cm = 12 cm - 4 cm = 8 cm

### Step 3: Calculate the volume of the outer box
The volume of the outer box can be calculated using the formula for the volume of a cuboid:
\[ \text{Volume}_{\text{outer}} = \text{Length} \times \text{Breadth} \times \text{Height} \]
\[ \text{Volume}_{\text{outer}} = 36 \, \text{cm} \times 24 \, \text{cm} \times 12 \, \text{cm} = 10368 \, \text{cm}^3 \]

### Step 4: Calculate the volume of the inner box
Using the inner dimensions calculated in Step 2:
\[ \text{Volume}_{\text{inner}} = \text{Inner Length} \times \text{Inner Breadth} \times \text{Inner Height} \]
\[ \text{Volume}_{\text{inner}} = 32 \, \text{cm} \times 20 \, \text{cm} \times 8 \, \text{cm} = 5120 \, \text{cm}^3 \]

### Step 5: Calculate the volume of the wood
The volume of the wood is the difference between the outer volume and the inner volume:
\[ \text{Volume}_{\text{wood}} = \text{Volume}_{\text{outer}} - \text{Volume}_{\text{inner}} \]
\[ \text{Volume}_{\text{wood}} = 10368 \, \text{cm}^3 - 5120 \, \text{cm}^3 = 5248 \, \text{cm}^3 \]

### Step 6: Convert the volume from cm³ to m³
To convert cubic centimeters to cubic meters, divide by \(100^3\) (since 1 m = 100 cm):
\[ \text{Volume}_{\text{wood}} = \frac{5248 \, \text{cm}^3}{100^3} = \frac{5248}{1000000} = 0.005248 \, \text{m}^3 \]

### Step 7: Calculate the weight of the wood
Using the density of the wood, which is given as 100 gm/m³, we can calculate the weight:
\[ \text{Weight} = \text{Density} \times \text{Volume}_{\text{wood}} \]
\[ \text{Weight} = 100 \, \text{gm/m}^3 \times 0.005248 \, \text{m}^3 = 0.5248 \, \text{gm} \]

### Final Answer
The weight of the wood used in the box is **0.5248 grams**.

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