To solve the problem step by step, we will calculate the capacity of the box, the volume of the wood used in making the box, and the weight of the box.
### Step 1: Calculate the External Volume of the Box
The external dimensions of the box are given as:
- Length (L1) = 30 cm
- Breadth (B1) = 18 cm
- Height (H1) = 20 cm
The external volume (V_external) of the box can be calculated using the formula for the volume of a cuboid:
\[
V_{\text{external}} = L1 \times B1 \times H1
\]
Substituting the values:
\[
V_{\text{external}} = 30 \, \text{cm} \times 18 \, \text{cm} \times 20 \, \text{cm}
\]
Calculating:
\[
V_{\text{external}} = 30 \times 18 = 540
\]
\[
540 \times 20 = 10800 \, \text{cm}^3
\]
### Step 2: Calculate the Internal Dimensions of the Box
The thickness of the walls is given as 1.5 cm. Therefore, we need to subtract twice the thickness from each external dimension to find the internal dimensions.
- Internal Length (L2):
\[
L2 = L1 - 2 \times \text{thickness} = 30 \, \text{cm} - 2 \times 1.5 \, \text{cm} = 30 - 3 = 27 \, \text{cm}
\]
- Internal Breadth (B2):
\[
B2 = B1 - 2 \times \text{thickness} = 18 \, \text{cm} - 2 \times 1.5 \, \text{cm} = 18 - 3 = 15 \, \text{cm}
\]
- Internal Height (H2):
\[
H2 = H1 - 2 \times \text{thickness} = 20 \, \text{cm} - 2 \times 1.5 \, \text{cm} = 20 - 3 = 17 \, \text{cm}
\]
### Step 3: Calculate the Internal Volume of the Box
Now we can calculate the internal volume (V_internal) using the internal dimensions:
\[
V_{\text{internal}} = L2 \times B2 \times H2
\]
Substituting the values:
\[
V_{\text{internal}} = 27 \, \text{cm} \times 15 \, \text{cm} \times 17 \, \text{cm}
\]
Calculating:
\[
27 \times 15 = 405
\]
\[
405 \times 17 = 6885 \, \text{cm}^3
\]
### Step 4: Calculate the Volume of the Wood Used
The volume of the wood used in making the box can be calculated by subtracting the internal volume from the external volume:
\[
V_{\text{wood}} = V_{\text{external}} - V_{\text{internal}}
\]
Substituting the values:
\[
V_{\text{wood}} = 10800 \, \text{cm}^3 - 6885 \, \text{cm}^3
\]
Calculating:
\[
V_{\text{wood}} = 3915 \, \text{cm}^3
\]
### Step 5: Calculate the Weight of the Box
The weight of the box can be calculated using the volume of the wood and the weight of 1 cm³ of wood (0.80 g):
\[
\text{Weight} = V_{\text{wood}} \times \text{weight per cm}^3
\]
Substituting the values:
\[
\text{Weight} = 3915 \, \text{cm}^3 \times 0.80 \, \text{g/cm}^3
\]
Calculating:
\[
\text{Weight} = 3132 \, \text{g}
\]
Converting grams to kilograms:
\[
\text{Weight} = 3.132 \, \text{kg}
\]
### Final Answers
(i) Capacity of the box: **6885 cm³**
(ii) Volume of the wood used: **3915 cm³**
(iii) Weight of the box: **3.132 kg**
