Circle – radius increased by 14%: If the radius of a circle increases by 14%, by what percentage does its area increase?

Introduction / Context:Area of a circle is proportional to the square of its radius. Therefore, any percentage change in radius compounds (squares) when translated to area. A 14% radius increase needs squaring of the scale factor 1.14.

Given Data / Assumptions:

• Original radius r; new radius = 1.14r.
• Area ∝ r^2.

Concept / Approach:New area / old area = (1.14)^2. The percentage increase in area is [(1.14)^2 − 1]*100%. Compute precisely to avoid rounding errors: 1.14^2 = 1.2996, which corresponds to a 29.96% rise.

Step-by-Step Solution:

Verification / Alternative check:Using binomial: (1 + 0.14)^2 = 1 + 2*0.14 + 0.14^2 = 1 + 0.28 + 0.0196 = 1.2996 → 29.96% increase.

Why Other Options Are Wrong:28% ignores the square term; 14% and 14.98% undercount; 28% + 1.96% = 29.96% is correct.

Common Pitfalls:Treating area change as linear in radius instead of quadratic.

Final Answer:29.96 percent