The radius of a circle is reduced from 9 cm to 7 cm. Find the percentage decrease in area (use π ≈ 22/7 as needed).

Introduction / Context:The area of a circle scales with the square of the radius: A ∝ r^2. Therefore, a change in radius from r1 to r2 changes the area by the ratio r2^2 / r1^2. The resulting percentage decrease follows from 1 − (new/old).

Given Data / Assumptions:

• Initial radius r1 = 9 cm
• New radius r2 = 7 cm
• Area is proportional to r^2

Concept / Approach:Compute the ratio of areas using squares of radii and convert to a percentage decrease. Constants like π cancel out, so no evaluation of π is required to get the percentage.

Step-by-Step Solution:Old area ∝ 9^2 = 81New area ∝ 7^2 = 49Fraction remaining = 49 / 81 ≈ 0.604938Percentage decrease = (1 − 49/81) * 100% = (32/81)*100% ≈ 39.5%

Verification / Alternative check:Approximation: Since 7/9 ≈ 0.777..., area scales by (7/9)^2 ≈ 0.6049; hence drop is about 39.51%, consistent with the exact fraction 32/81 ≈ 0.39506.

Why Other Options Are Wrong:31.5% and 34.5% undervalue the squared effect; 65.5% is far too large and would imply the new area is only 34.5% of the old area, which is not true for 7 vs 9 cm radii.

Common Pitfalls:Using linear rather than squared scaling or accidentally computing (9 − 7)/9 as the area decrease. Area depends on r^2, not r.

Final Answer:39.5 %