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.