Which is false? Write the correct answer.
A metal pipe is 63cm long. Its inner diameter is 4cm and the outer diameter is 4.4 cm. then

Options

A. Its inner cuved surface area`=792cm^(2)`
B. Its outer curved surface area`=871.2cm^(2)`
C. Surface area of each end=`2.64cm^(2)`
D. Its total surface area=`1665.84cm^(2)`

Answer

To solve the problem step-by-step, we will analyze the given information about the metal pipe and calculate the required surface areas to identify which statement is false.

### Step 1: Identify the given dimensions
- Length of the pipe (L) = 63 cm
- Inner diameter (d) = 4 cm
- Outer diameter (D) = 4.4 cm

### Step 2: Calculate the inner radius
The inner radius (r) can be calculated as:
\[ r = \frac{d}{2} = \frac{4 \text{ cm}}{2} = 2 \text{ cm} \]

### Step 3: Calculate the outer radius
The outer radius (R) can be calculated as:
\[ R = \frac{D}{2} = \frac{4.4 \text{ cm}}{2} = 2.2 \text{ cm} \]

### Step 4: Calculate the inner curved surface area
The formula for the inner curved surface area (CSA) is:
\[ \text{Inner CSA} = 2 \pi r L \]
Substituting the values:
\[ \text{Inner CSA} = 2 \times \frac{22}{7} \times 2 \text{ cm} \times 63 \text{ cm} \]
Calculating this:
\[ = 2 \times \frac{22}{7} \times 2 \times 63 = \frac{88 \times 63}{7} = \frac{5544}{7} \approx 792 \text{ cm}^2 \]

### Step 5: Calculate the outer curved surface area
The formula for the outer curved surface area (CSA) is:
\[ \text{Outer CSA} = 2 \pi R L \]
Substituting the values:
\[ \text{Outer CSA} = 2 \times \frac{22}{7} \times 2.2 \text{ cm} \times 63 \text{ cm} \]
Calculating this:
\[ = 2 \times \frac{22}{7} \times 2.2 \times 63 = \frac{88 \times 2.2 \times 63}{7} = \frac{11088}{7} \approx 871.2 \text{ cm}^2 \]

### Step 6: Calculate the surface area of each end
The surface area of each end is given by:
\[ \text{Area of each end} = \pi (R^2 - r^2) \]
Calculating this:
\[ = \frac{22}{7} \left( (2.2)^2 - (2)^2 \right) = \frac{22}{7} \left( 4.84 - 4 \right) = \frac{22}{7} \times 0.84 \]
Calculating this:
\[ = \frac{22 \times 0.84}{7} = \frac{18.48}{7} \approx 2.64 \text{ cm}^2 \]

### Step 7: Calculate the total surface area
The total surface area (TSA) is given by:
\[ \text{TSA} = \text{Inner CSA} + \text{Outer CSA} + 2 \times \text{Area of each end} \]
Substituting the values:
\[ \text{TSA} = 792 + 871.2 + 2 \times 2.64 \]
Calculating this:
\[ = 792 + 871.2 + 5.28 = 1668.48 \text{ cm}^2 \]

### Step 8: Identify the false statement
If the total surface area given in the options is 1665 cm², then it is incorrect. The correct total surface area is approximately 1668.48 cm².

### Conclusion
The false statement is the one that claims the total surface area is 1665 cm². The correct answer is approximately 1668.48 cm².

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