If the radius of a circle is increased by 10%, its area will increase by—
21%
Let the original radius = r, so original area = πr². When the radius is increased by 10%, new radius = 1.1r. New area = π(1.1r)² = π × 1.21r² = 1.21πr². Increase in area = 0.21πr². Percentage increase = (0.21 ÷ 1) × 100 = 21%. A common error is to assume a 10% or 20% increase — area scales as the square of the radius, not linearly.
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