If the curved surface area of the cylinder is `440 cm^(2)` and the height of the cylinder is 10 cm, then what is the radius (in cm) of the cylinder ?

Options

A. 7
B. 14
C. 21
D. `3.5`

Answer

To find the radius of the cylinder given its curved surface area and height, we can use the formula for the curved surface area (CSA) of a cylinder:

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

Where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.

Given:
- Curved Surface Area (CSA) = 440 cm²,
- Height (h) = 10 cm.

### Step-by-Step Solution:

1. **Write down the formula for the curved surface area of a cylinder:**
\[ CSA = 2 \pi r h \]

2. **Substitute the known values into the formula:**
\[ 440 = 2 \pi r (10) \]

3. **Simplify the equation:**
\[ 440 = 20 \pi r \]

4. **To isolate \( r \), divide both sides by \( 20 \pi \):**
\[ r = \frac{440}{20 \pi} \]

5. **Substituting the value of \( \pi \) (using \( \pi \approx \frac{22}{7} \)):**
\[ r = \frac{440}{20 \times \frac{22}{7}} \]

6. **Calculate \( 20 \times \frac{22}{7} \):**
\[ 20 \times \frac{22}{7} = \frac{440}{7} \]

7. **Now substitute this back into the equation for \( r \):**
\[ r = \frac{440 \times 7}{440} = 7 \]

8. **Thus, the radius of the cylinder is:**
\[ r = 7 \text{ cm} \]

### Final Answer:
The radius of the cylinder is \( 7 \) cm.