If the curved surface area of a 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`

Explanation

To find the radius 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 know the curved surface area is \( 440 \, \text{cm}^2 \) and the height \( H \) is \( 10 \, \text{cm} \). Substitute these values into the formula:
\[ 440 = 2 \pi R \times 10 \]

3. **Simplify the Equation**:
We can simplify the equation:
\[ 440 = 20 \pi R \]

4. **Isolate the Radius \( R \)**:
To find \( R \), we need to isolate it. First, divide both sides by \( 20 \pi \):
\[ R = \frac{440}{20 \pi} \]

5. **Substitute the Value of \( \pi \)**:
Using \( \pi \approx \frac{22}{7} \):
\[ R = \frac{440}{20 \times \frac{22}{7}} \]

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

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

8. **Conclusion**:
Therefore, the radius \( R \) of the cylinder is:
\[ R = 7 \, \text{cm} \]