The curved surface area of a cylinder is 110 `cm^(2)` and its diameter is 7 cm. Find the height of the cylinder.

Answer

To find the height of the cylinder given its curved surface area and diameter, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Curved Surface Area (CSA) of the cylinder = 110 cm²
- Diameter of the cylinder = 7 cm

2. **Calculate the radius of the cylinder:**
- The radius (r) is half of the diameter.
\[ r = \frac{\text{Diameter}}{2} = \frac{7 \text{ cm}}{2} = 3.5 \text{ cm} \]

3. **Use the formula for the curved surface area of a cylinder:**
- The formula for the curved surface area (CSA) of a cylinder is given by:
\[ \text{CSA} = 2\pi rh \]
where \( h \) is the height of the cylinder.

4. **Substitute the known values into the formula:**
- We know CSA = 110 cm² and \( r = 3.5 \) cm. Substitute these values into the formula:
\[ 110 = 2 \times \pi \times 3.5 \times h \]

5. **Use the approximate value of \( \pi \):**
- For calculations, we can use \( \pi \approx \frac{22}{7} \):
\[ 110 = 2 \times \frac{22}{7} \times 3.5 \times h \]

6. **Simplify the equation:**
- First, calculate \( 2 \times \frac{22}{7} \times 3.5 \):
\[ 2 \times \frac{22}{7} \times 3.5 = 2 \times \frac{22 \times 3.5}{7} = 2 \times \frac{77}{7} = \frac{154}{7} \]
- Now, substitute this back into the equation:
\[ 110 = \frac{154}{7} \times h \]

7. **Isolate \( h \):**
- To find \( h \), multiply both sides by \( \frac{7}{154} \):
\[ h = 110 \times \frac{7}{154} \]

8. **Calculate \( h \):**
- Simplify the right-hand side:
\[ h = \frac{770}{154} \]
- Now, divide:
\[ h = 5 \text{ cm} \]

### Final Answer:
The height of the cylinder is **5 cm**.