Circle – radius reduced by half: If the radius of a circle is decreased by 50%, what is the percentage decrease in its area?

Introduction / Context:Area of a circle depends on the square of the radius. A percentage change in radius does not translate linearly to area.

Given Data / Assumptions:

• Original radius = r.
• New radius = 0.5*r.

Concept / Approach:Area ∝ r^2. New area = (0.5)^2 times old area = 0.25 of original. Decrease = 75%.

Step-by-Step Solution:

Verification / Alternative check:Pick r = 10 → original area 100π; new radius 5 → new area 25π. Drop = 75π → 75%.

Why Other Options Are Wrong:65%, 35%, 25% are linear-style misreads; area scales quadratically, not linearly.

Common Pitfalls:Applying 50% directly to area instead of squaring the radius factor.

Final Answer:75%