Spheres — Radii in ratio 1:2. What is the ratio of their surface areas?

Introduction / Context:
Surface area of a sphere S = 4πr^2, so areas scale with r^2.

Given Data / Assumptions:

• r1:r2 = 1:2

Concept / Approach:
S1:S2 = r1^2:r2^2 = 1^2:2^2 = 1:4.

Step-by-Step Solution:
S1:S2 = 1:4

Verification / Alternative check:
Pick radii 1 and 2; compute 4π and 16π.

Why Other Options Are Wrong:
1:2 uses linear scale; 1:√2 mixes up radius with area ratio; others are unrelated.

Common Pitfalls:
Forgetting the square in surface area.

Final Answer:
1 : 4