To find the weight of the wooden box, we will follow these steps:
### Step 1: Calculate the External Volume of the Box
The external dimensions of the box are given as:
- Length (L) = 20 cm
- Width (W) = 10 cm
- Height (H) = 9 cm
The formula for the volume of a rectangular box is:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the values:
\[ \text{External Volume} = 20 \, \text{cm} \times 10 \, \text{cm} \times 9 \, \text{cm} = 1800 \, \text{cm}^3 \]
### Step 2: Calculate the Internal 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 internal dimensions:
- Internal Length = \( 20 - 2 \times 1 = 18 \, \text{cm} \)
- Internal Width = \( 10 - 2 \times 1 = 8 \, \text{cm} \)
- Internal Height = \( 9 - 2 \times 1 = 7 \, \text{cm} \)
### Step 3: Calculate the Internal Volume of the Box
Now, we can calculate the internal volume using the internal dimensions:
\[ \text{Internal Volume} = \text{Internal Length} \times \text{Internal Width} \times \text{Internal Height} \]
\[ \text{Internal Volume} = 18 \, \text{cm} \times 8 \, \text{cm} \times 7 \, \text{cm} = 1008 \, \text{cm}^3 \]
### Step 4: Calculate the Volume of the Wood
To find the volume of the wood, we subtract the internal volume from the external volume:
\[ \text{Volume of Wood} = \text{External Volume} - \text{Internal Volume} \]
\[ \text{Volume of Wood} = 1800 \, \text{cm}^3 - 1008 \, \text{cm}^3 = 792 \, \text{cm}^3 \]
### Step 5: Calculate the Weight of the Wood
We know that 1 cm³ of wood weighs 0.5 g. Therefore, to find the weight of the wood, we multiply the volume of the wood by the weight per cm³:
\[ \text{Weight of Wood} = \text{Volume of Wood} \times \text{Weight per cm}^3 \]
\[ \text{Weight of Wood} = 792 \, \text{cm}^3 \times 0.5 \, \text{g/cm}^3 = 396 \, \text{g} \]
### Final Answer
The weight of the wooden box is **396 grams**.
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