The curved surface area of cyclinder of height 14 cm is ` 88 cm ^(2) `. Find the diameter of the base of the cyclinder.

Answer

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

### Step-by-Step Solution:

1. **Understand the Formula for Curved Surface Area of a Cylinder**:
The formula for the curved surface area (CSA) of a cylinder is given by:
\[ \text{CSA} = 2 \pi r h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.

2. **Substitute the Given Values**:
We are given:
- Curved Surface Area (CSA) = 88 cm²
- Height (h) = 14 cm
We can substitute these values into the formula:
\[ 88 = 2 \pi r \times 14 \]

3. **Simplify the Equation**:
First, we can simplify the equation:
\[ 88 = 28 \pi r \]
Now, we can solve for \( r \):
\[ r = \frac{88}{28 \pi} \]

4. **Use Approximation for π**:
For calculations, we can use \( \pi \approx \frac{22}{7} \):
\[ r = \frac{88}{28 \times \frac{22}{7}} = \frac{88 \times 7}{28 \times 22} \]

5. **Perform the Calculations**:
Simplifying the fraction:
- \( 88 \div 28 = 3.14 \) (approximately)
- \( 7 \div 22 = 0.318 \) (approximately)
Therefore:
\[ r \approx 1 \text{ cm} \]

6. **Find the Diameter**:
The diameter \( d \) of the cylinder is given by:
\[ d = 2r \]
Substituting the value of \( r \):
\[ d = 2 \times 1 = 2 \text{ cm} \]

### Final Answer:
The diameter of the base of the cylinder is **2 cm**.

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