A metal pipe of negligible thickness has radius 21 cm and length 90 cm. The outer curved surface area of the pipe in square cm is

Options

A. 11880
B. 11680
C. 11480
D. 10080

Answer

To find the outer curved surface area of a metal pipe, we can use the formula for the curved surface area of a cylinder, which is given by:

\[ \text{Curved Surface Area} = 2 \pi r h \]

where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height (or length) of the cylinder.

### Step-by-Step Solution:

1. **Identify the given values:**
- Radius \( r = 21 \) cm
- Length \( h = 90 \) cm

2. **Substitute the values into the formula:**
\[ \text{Curved Surface Area} = 2 \pi r h \]
\[ = 2 \times \pi \times 21 \times 90 \]

3. **Use the value of \( \pi \):**
For simplicity, we can use \( \pi \approx \frac{22}{7} \):
\[ = 2 \times \frac{22}{7} \times 21 \times 90 \]

4. **Calculate the expression:**
- First, calculate \( 2 \times \frac{22}{7} \):
\[ = \frac{44}{7} \]
- Now, multiply by \( 21 \):
\[ = \frac{44 \times 21}{7} \]
- Since \( 21 \div 7 = 3 \):
\[ = 44 \times 3 = 132 \]
- Now multiply by \( 90 \):
\[ = 132 \times 90 \]

5. **Final multiplication:**
\[ = 11880 \text{ cm}^2 \]

Thus, the outer curved surface area of the pipe is **11880 cm²**.