If the outer diameter of metal pipe is 4cm and inner diameter is 3cm. Its length is 20cm, then the volume of metal used is

Options

A. `220cm^(3)`
B. `110cm^(3)`
C. `22cm^(3)`
D. `440cm^(3)`

Answer

To find the volume of the metal used in the hollow cylinder (metal pipe), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given dimensions:**
- Outer diameter of the pipe = 4 cm
- Inner diameter of the pipe = 3 cm
- Length of the pipe (height) = 20 cm

2. **Calculate the radii:**
- Outer radius (R) = Outer diameter / 2 = 4 cm / 2 = 2 cm
- Inner radius (r) = Inner diameter / 2 = 3 cm / 2 = 1.5 cm

3. **Use the formula for the volume of a hollow cylinder:**
\[ V = \pi (R^2 - r^2) h \]
where:
- \( R \) = outer radius
- \( r \) = inner radius
- \( h \) = height (length of the pipe)

4. **Substitute the values into the formula:**
\[ V = \pi (2^2 - 1.5^2) \times 20 \]

5. **Calculate the squares of the radii:**
- \( R^2 = 2^2 = 4 \)
- \( r^2 = 1.5^2 = 2.25 \)

6. **Subtract the inner radius square from the outer radius square:**
\[ R^2 - r^2 = 4 - 2.25 = 1.75 \]

7. **Substitute back into the volume formula:**
\[ V = \pi \times 1.75 \times 20 \]

8. **Calculate the volume:**
\[ V = \pi \times 35 \]
Using \( \pi \approx \frac{22}{7} \):
\[ V = \frac{22}{7} \times 35 \]

9. **Perform the multiplication:**
\[ V = \frac{770}{7} \approx 110 \text{ cm}^3 \]

### Final Answer:
The volume of metal used in the pipe is approximately \( 110 \text{ cm}^3 \).