Largest circle on a sphere — compute diameter from sphere surface area: The surface area of a sphere is 616 sq cm. What is the diameter of the largest circle lying on its surface (i.e., the great circle)?

Introduction / Context:
The largest circle on a sphere is a great circle whose diameter equals the sphere’s diameter. Therefore, determining the sphere’s radius from its surface area directly gives the required diameter.

Given Data / Assumptions:

• Sphere surface area S = 4πr^2 = 616 cm2.
• Standard school setting typically uses π = 22/7 for such integer-friendly values.

Concept / Approach:
Solve for r^2 = 616 / (4π). With π = 22/7, arithmetic becomes exact and yields an integer r. The great-circle diameter equals 2r.

Step-by-Step Solution:
r^2 = 616 / (4π) = 154 / πUsing π = 22/7 ⇒ r^2 = 154 * 7 / 22 = 49r = 7 cm ⇒ diameter = 2r = 14 cm

Verification / Alternative check:
Back substitute: 4πr^2 = 4*(22/7)*49 = 616 cm2, matching.

Why Other Options Are Wrong:
10.5 cm is the radius, not the diameter; 7 cm and 3.5 cm are radius and half-radius magnitudes.

Common Pitfalls:
Confusing surface area with cross-sectional (circle) area; forgetting the great circle’s diameter equals the sphere’s diameter.

Final Answer:
14 cm