On decreasing the radius of a circle by 30%, its area is decreased by

Let the radius if circle be r

Area of circle = A = πr^{2}

Radius decreases by 30%

So, New Radius r’ = r - 30/100 × r = 0.7r

New Area of circle = A’ = πr’^{2} = π × (0.7r)^{2}

= .49πr^{2}

Percentage decrease in area =

= = .51 × 100 = 51

∴ Decrease in area = 51%

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