A metal pipe in 77 cm long. If the inner diameter ofa cross section is 4 cm and the outer diameter being 4.4 cm. Then, its outer curved surface area is

Options

A. 1164.8 `cm^2`
B. 1440.8 `cm^2`
C. 123.8 `cm^2`
D. 1064.8 `cm^2`

Answer

To find the outer curved surface area of the metal pipe, we can follow these steps:

### Step 1: Identify the given dimensions
- Length of the pipe (h) = 77 cm
- Outer diameter (D) = 4.4 cm

### Step 2: Calculate the outer radius (r)
The radius is half of the diameter:
\[ r = \frac{D}{2} = \frac{4.4 \, \text{cm}}{2} = 2.2 \, \text{cm} \]

### Step 3: Use the formula for the curved surface area of a cylinder
The formula for the curved surface area (CSA) of a cylinder is:
\[ \text{CSA} = 2 \pi r h \]

### Step 4: Substitute the values into the formula
Using \( \pi \approx \frac{22}{7} \):
\[ \text{CSA} = 2 \times \frac{22}{7} \times 2.2 \, \text{cm} \times 77 \, \text{cm} \]

### Step 5: Simplify the expression
Calculate \( 2 \times 2.2 = 4.4 \):
\[ \text{CSA} = \frac{22}{7} \times 4.4 \times 77 \]

### Step 6: Calculate \( 4.4 \times 77 \)
\[ 4.4 \times 77 = 338.8 \]

### Step 7: Substitute back into the equation
Now we have:
\[ \text{CSA} = \frac{22}{7} \times 338.8 \]

### Step 8: Multiply and simplify
Calculating \( 22 \times 338.8 = 7453.6 \):
\[ \text{CSA} = \frac{7453.6}{7} \]

### Step 9: Final calculation
Now divide:
\[ \text{CSA} = 1064.8 \, \text{cm}^2 \]

Thus, the outer curved surface area of the metal pipe is **1064.8 cm²**.

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