Effect of Doubling Diameter on Circle Area — Percent Increase: If the diameter of a circle is increased by 100% (i.e., doubled), by what percent does its area increase?

Introduction / Context:Circle area depends on the square of a linear dimension (radius or diameter). Doubling the diameter doubles the radius as well, so the area multiplies by 2^2 = 4. Converting that factor to a percentage increase distinguishes absolute area from relative change.

Given Data / Assumptions:

• Original diameter D; new diameter = 2D
• Original radius r = D/2; new radius r' = D
• Area formula: A = πr^2

Concept / Approach:Compute the factor by which area changes: A'/A = (r'^2)/(r^2) = (D^2)/(D^2/4) = 4. A factor of 4 corresponds to a 300% increase because Increase% = (new − old)/old * 100% = (4A − A)/A * 100% = 300%.

Step-by-Step Solution:

Verification / Alternative check:

Why Other Options Are Wrong:

• 100% implies doubling area, not quadrupling.
• 200% implies tripling total, still short of 4A.
• 400% confuses new area with the percent increase.
• 150% is arbitrary and unsupported.

Common Pitfalls:

• Reporting the new area as 400% instead of the increase of 300%.

Final Answer:300% increase.