A lead pencil is in the shape of right circular cylinder. The pencil is 28 cm long and its radius is 3 mm. If the lead is of radius 1 mm, the volume of the wood used is:

Options

A. `0.352 cm^(3)`
B. `7.04 cm^(3)`
C. `3.52 cm^(3)`
D. `70.4 cm^(3)`

Answer

To find the volume of wood used in the pencil, we need to calculate the volume of the outer cylinder (the entire pencil) and subtract the volume of the inner cylinder (the lead).

### Step-by-Step Solution:

1. **Identify the dimensions:**
- Length of the pencil (h) = 28 cm
- Outer radius of the pencil (R) = 3 mm = 0.3 cm (since 1 cm = 10 mm)
- Inner radius of the lead (r) = 1 mm = 0.1 cm

2. **Calculate the volume of the outer cylinder (pencil):**
The formula for the volume of a cylinder is:
\[ V = \pi R^2 h \]
Substituting the values:
\[ V_{\text{pencil}} = \pi (0.3)^2 (28) \]
\[ V_{\text{pencil}} = \pi (0.09) (28) \]
\[ V_{\text{pencil}} = 2.52\pi \, \text{cm}^3 \]

3. **Calculate the volume of the inner cylinder (lead):**
Using the same formula for the volume:
\[ V_{\text{lead}} = \pi r^2 h \]
Substituting the values:
\[ V_{\text{lead}} = \pi (0.1)^2 (28) \]
\[ V_{\text{lead}} = \pi (0.01) (28) \]
\[ V_{\text{lead}} = 0.28\pi \, \text{cm}^3 \]

4. **Calculate the volume of wood used:**
The volume of wood is the difference between the volume of the pencil and the volume of the lead:
\[ V_{\text{wood}} = V_{\text{pencil}} - V_{\text{lead}} \]
\[ V_{\text{wood}} = 2.52\pi - 0.28\pi \]
\[ V_{\text{wood}} = (2.52 - 0.28)\pi \]
\[ V_{\text{wood}} = 2.24\pi \, \text{cm}^3 \]

5. **Calculate the numerical value:**
Using \(\pi \approx \frac{22}{7}\):
\[ V_{\text{wood}} = 2.24 \times \frac{22}{7} \]
\[ V_{\text{wood}} \approx 7.04 \, \text{cm}^3 \]

### Final Answer:
The volume of wood used in the pencil is approximately **7.04 cm³**.