A circular disc's radius is decreased by 10%. What is the percentage decrease in its area?

Correct — B. Area = πr², so the area changes with the square of the radius.

Cut the radius by 10%: new radius = 0.9r
Square it: new area = π(0.9r)² = 0.81πr²
Subtract: decrease = 1 − 0.81 = 0.19 = 19% → option (b)

Shortcut: −10 − 10 + (−10)(−10) ÷ 100 = −19%.

Why the others are wrong

• (a)
  10% — 10% is the change in the radius, not in the area. Area goes with r², so the 0.9 factor applies twice: 0.9 × 0.9 = 0.81.
• (c)
  18% — An 18% fall leaves 82% of the area, which needs a radius of √0.82 ≈ 0.906 times the old one, a cut of about 9.4%, not 10%.
• (d)
  15% — A 15% fall leaves 85% of the area, which matches a radius cut of only about 7.8% (√0.85 ≈ 0.922), not 10%.

When every length of a flat shape is scaled by a factor k, its area is scaled by k². A 10% cut makes k = 0.9, so the area becomes 0.81 of what it was.

The successive-change formula gives the same result: changes of a% and b% combine to a + b + ab ⁄ 100. With a = b = −10 that is −19%.

Key facts

• A factor k on every length of a flat shape multiplies its area by k².
• Two successive percentage changes a% and b% combine to a + b + ab ⁄ 100.
• A 10% cut in radius leaves 0.9² = 0.81 of the area, a 19% decrease.

Common traps

• Carrying the 10% straight across to the area, which treats area as proportional to r rather than r².
• Writing −10 − 10 = −20% and dropping the +1 that comes from (−10)(−10) ÷ 100.

No directly related past PYQ was found.