1. Identify the Question Type: This is a Mensuration problem involving the surface area of a sphere.

2. Step-by-Step Solution:

• Find the radius: The diameter of the sphere is given as 98 cm. The radius (r) is half the diameter, so \(r = \frac{98}{2} = 49\) cm.
• Formula for Surface Area: The formula for the surface area (A) of a sphere is \(A = 4\pi r^2\).
• Substitute and Calculate: Substitute the value of the radius (r = 49 cm) into the formula:
• \(A = 4 \times \pi \times (49)^2\)
• \(A = 4 \times \pi \times 2401\)
• Using \(\pi = \frac{22}{7}\), we get:
• \(A = 4 \times \frac{22}{7} \times 2401\)
• \(A = 4 \times 22 \times 343\)
• \(A = 88 \times 343\)
• \(A = 30184\) cm²

3. Core Logic/Pattern: The core logic is applying the correct formula for the surface area of a sphere and performing the calculation accurately.

4. Eliminate Incorrect Options: The incorrect options (29256, 39204, 33284) result from calculation errors or using an incorrect formula. They are not the result of the correct application of the surface area formula for a sphere.

5. Conclusion: The surface area of the sphere is 30,184 cm².