If `1 cm^(3)` of cast iron weights 21g, find the weight of a cast iron pipe of length 1m with a bore of 3 cm in which the thickness of the metal is 1cm.

Explanation

To solve the problem, we need to find the weight of a cast iron pipe given its dimensions and the weight of cast iron per unit volume. Here’s a step-by-step solution:

### Step 1: Understand the Dimensions of the Pipe
- The bore (inner diameter) of the pipe is given as 3 cm. Therefore, the inner radius \( r_i \) is:
\[ r_i = \frac{3}{2} = 1.5 \text{ cm} \]

- The thickness of the metal is 1 cm, so the outer radius \( r_o \) is:
\[ r_o = r_i + \text{thickness} = 1.5 + 1 = 2.5 \text{ cm} \]

- The length of the pipe is given as 1 m, which is:
\[ h = 100 \text{ cm} \quad (\text{since } 1 \text{ m} = 100 \text{ cm}) \]

### Step 2: Calculate the Volume of the Pipe
The volume \( V \) of the pipe can be calculated by finding the volume of the outer cylinder and subtracting the volume of the inner cylinder.

1. **Volume of the outer cylinder**:
\[ V_o = \pi r_o^2 h = \pi (2.5)^2 (100) = \pi (6.25)(100) = 625\pi \text{ cm}^3 \]

2. **Volume of the inner cylinder**:
\[ V_i = \pi r_i^2 h = \pi (1.5)^2 (100) = \pi (2.25)(100) = 225\pi \text{ cm}^3 \]

3. **Volume of the pipe**:
\[ V = V_o - V_i = 625\pi - 225\pi = 400\pi \text{ cm}^3 \]

### Step 3: Calculate the Weight of the Pipe
Now, we can find the weight of the cast iron pipe using the volume we calculated and the weight of cast iron per cubic centimeter.

- The weight of 1 cm³ of cast iron is given as 21 g. Therefore, the weight \( W \) of the pipe is:
\[ W = V \times \text{weight per cm}^3 = 400\pi \times 21 \]

### Step 4: Calculate the Final Weight
Now we can compute the weight:
\[ W = 400 \times 3.14 \times 21 \approx 400 \times 66.94 \approx 26776 \text{ g} \approx 26.776 \text{ kg} \]

### Final Answer
The weight of the cast iron pipe is approximately **26.776 kg**.