The surface area of a sphere is 6.16 square centimetres. What is the diameter (in cm) of the sphere?

Introduction / Context:
This is a mensuration question involving a sphere. You are given the total surface area and asked to find the diameter. To answer, you must recall the formula for the surface area of a sphere and then work backward to find the radius and diameter.

Given Data / Assumptions:

• Surface area of the sphere S = 6.16 square cm.
• Surface area formula: S = 4 * π * r^2.
• We assume π is approximately 3.14 for numerical evaluation.
• We need the diameter, which equals 2r.

Concept / Approach:
The relationship between surface area and radius for a sphere is S = 4 * π * r^2. Given S, we solve for r^2 = S / (4 * π). Taking the square root gives r, and then we multiply by 2 to get the diameter. Finally, we match the calculated value to the closest option.

Step-by-Step Solution:
Step 1: Use S = 4 * π * r^2.Step 2: Substitute S = 6.16 and π ≈ 3.14: 6.16 = 4 * 3.14 * r^2.Step 3: Compute the denominator: 4 * 3.14 = 12.56.Step 4: Solve for r^2: r^2 = 6.16 / 12.56 ≈ 0.49.Step 5: Take the square root: r ≈ √0.49 = 0.7 cm.Step 6: Diameter d = 2 * r = 2 * 0.7 = 1.4 cm.

Verification / Alternative check:
Substitute r = 0.7 back into the surface area formula: S = 4 * 3.14 * 0.7^2 = 4 * 3.14 * 0.49 ≈ 6.16 square cm, which matches the given surface area and confirms that the diameter is correct.

Why Other Options Are Wrong:
0.7 cm is the radius, not the diameter. The options 2.1 cm, 2.8 cm and 3.5 cm all correspond to larger radii, which would produce much larger surface areas than 6.16 square cm.

Common Pitfalls:
Students often forget to double the radius to obtain the diameter, or they invert the formula incorrectly. Another common error is rounding too early instead of keeping sufficient precision until the final step.

Final Answer:
The diameter of the sphere is 1.4 cm.