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To solve this problem, let's recall the formula for the total surface area of a cone, which is:

\[
\text{Total Surface Area} = \pi r (r + l)
\]

where:
- \( r \) is the radius of the cone,
- \( l \) is the slant height of the cone.

Given:
- Slant height (\( l \)) = 25 cm
- Total surface area = 704 cm²

We need to find the radius \( r \).

### Step-by-Step Solution:
1. Plug the values into the formula:
   \[
   704 = \pi r (r + 25)
   \]

2. Divide both sides by \( \pi \) (approximately 3.1416):
   \[
   \frac{704}{\pi} = r (r + 25)
   \]

   \[
   224.47 \approx r^2 + 25r
   \]

3. Rearrange into a quadratic equation:
   \[
   r^2 + 25r - 224.47 = 0
   \]

4. Use the quadratic formula:
   \[
   r = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
   \]
   where \( a = 1 \), \( b = 25 \), and \( c = -224.47 \).

   \[
   r = \frac{-25 \pm \sqrt{(25)^2 - 4 \times 1 \times (-224.47)}}{2 \times 1}
   \]

   \[
   r = \frac{-25 \pm \sqrt{625 + 897.88}}{2}
   \]

   \[
   r = \frac{-25 \pm \sqrt{1522.88}}{2}
   \]

   \[
   r = \frac{-25 \pm 39.03}{2}
   \]

5. Solving for \( r \), we get two values:
   - \( r = \frac{14.03}{2} = 7.015 \approx 7 \, \text{cm} \)
   - \( r = \frac{-64.03}{2} = -32.015 \, \text{(not possible as radius can't be negative)} \)

Therefore, the correct answer is:
\[
\boxed{7 \, \text{cm}}
\]

The answer is (A) 7 cm.

Would you like more details, or have any questions on this? 

Here are 5 related questions you might find interesting:
1. What is the formula for the volume of a cone?
2. How can you find the slant height of a cone if the radius and height are known?
3. What is the lateral surface area of a cone?
4. How would the formula change if the cone were truncated?
5. What happens to the surface area if the radius doubles?

**Tip:** Always check units and simplify calculations whenever possible for easier processing.

If the total surface area of a cone of slant height 25 cm is 704 cm², then find its radius.

Learn how to determine the radius of a cone when the total surface area is 704 cm² and the slant height is 25 cm. This solution involves using the surface area formula and solving a quadratic equation, making it ideal for students in Grades 9-10.

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