Effect on area when radius is reduced to 25% If the radius of a circle becomes 25% of its original value, by what percentage does the area decrease?

Introduction / Context:Area of a circle scales with the square of its radius. If the radius is scaled by a factor k, the area scales by k^2. Here, reducing radius to 25% means k = 0.25, so the area greatly diminishes.

Given Data / Assumptions:

• New radius r2 = 0.25 * r1
• Area scales as A ∝ r^2

Concept / Approach:Compute the new-to-old area ratio: (r2/r1)^2 = (0.25)^2 = 0.0625. That means the new area is 6.25% of the original, so the decrease is 100% − 6.25% = 93.75%.

Step-by-Step Solution:

Verification / Alternative check:Take a concrete example: original radius = 4 ⇒ area = 16π. New radius = 1 ⇒ area = π. Decrease = 15π out of 16π ≈ 93.75%, confirming the proportion.

Why Other Options Are Wrong:25% and 50% ignore the square scaling; 43.75% is half of the correct decrease; only 93.75% matches k^2 scaling.

Common Pitfalls:Applying linear rather than quadratic scaling to area leads to significant underestimation of the decrease.

Final Answer:93.75%