The surface area of a sphere is 5544 square centimetres. Using π = 22/7, what is the diameter of the sphere in centimetres?

Introduction / Context:
This question involves the formula for the surface area of a sphere and asks you to find the diameter. Spheres are common in geometry and physics, and knowing how to move between radius, diameter and surface area using the standard formulas is important for many quantitative exams.

Given Data / Assumptions:
- Surface area of the sphere S = 5544 square centimetres.
- Use π = 22 / 7 as indicated by the problem style, which is common in aptitude questions.
- We need to find the diameter of the sphere in centimetres.

Concept / Approach:
The surface area S of a sphere with radius r is given by:
S = 4 * π * r^2
Once we know S and π, we can rearrange this formula to solve for r^2 and then r. The diameter D is simply 2r. So the main steps are to find r from the given area and then double r to get the diameter.

Step-by-Step Solution:
Step 1: Write the surface area formula S = 4 * π * r^2. Step 2: Substitute S = 5544 and π = 22 / 7 into the equation: 5544 = 4 * (22 / 7) * r^2. Step 3: Compute the constant part: 4 * (22 / 7) = 88 / 7. Step 4: So 5544 = (88 / 7) * r^2, which implies r^2 = 5544 * 7 / 88. Step 5: Simplify 5544 / 88 = 63, so r^2 = 63 * 7 = 441. Therefore r = √441 = 21 cm, and the diameter D = 2 * 21 = 42 cm.

Verification / Alternative check:
Substitute r = 21 cm back into the formula to verify. S = 4 * π * r^2 = 4 * 22 / 7 * 21^2. First compute 21^2 = 441. Then S = 4 * 22 / 7 * 441 = 4 * 22 * 63 = 88 * 63 = 5544, which exactly matches the given surface area. This confirms that r = 21 cm and D = 42 cm are correct.

Why Other Options Are Wrong:
A diameter of 21 cm would correspond to a radius of 10.5 cm and a much smaller surface area.
84 cm and 63 cm would correspond to radii that produce surface areas very different from 5544 square centimetres.
28 cm would give radius 14 cm and again an incorrect surface area when substituted into the formula.

Common Pitfalls:
Students sometimes confuse diameter and radius, using r instead of 2r when reading the answer choices. Another common error is not simplifying the fraction correctly when solving for r^2. Careful arithmetic and clear separation of each step help avoid these issues.

Final Answer:
The diameter of the sphere is 42 cm.