The curved surface area of a cone is 628 `cm^(2)` and its slant height is 20 cm. Find its radius. `(pi=3.14)`

Answer

To find the radius of the cone given its curved surface area (CSA) and slant height, we can follow these steps:

### Step-by-Step Solution:

1. **Write down the formula for the curved surface area of a cone:**
\[ \text{CSA} = \pi r l \]
where \( r \) is the radius and \( l \) is the slant height.

2. **Substitute the known values into the formula:**
Given:
- Curved Surface Area (CSA) = 628 cm²
- Slant Height (l) = 20 cm
- \( \pi = 3.14 \)

The equation becomes:
\[ 628 = 3.14 \times r \times 20 \]

3. **Simplify the equation:**
First, calculate \( 3.14 \times 20 \):
\[ 3.14 \times 20 = 62.8 \]
Now, the equation is:
\[ 628 = 62.8 \times r \]

4. **Isolate \( r \):**
To find \( r \), divide both sides by 62.8:
\[ r = \frac{628}{62.8} \]

5. **Perform the division:**
To simplify \( \frac{628}{62.8} \), we can eliminate the decimal by multiplying both the numerator and denominator by 10:
\[ r = \frac{6280}{628} \]
Now, perform the division:
\[ r = 10 \]

6. **State the final answer:**
The radius \( r \) of the cone is:
\[ r = 10 \text{ cm} \]