the diameter of a circle is increased by 15%.what is the percentage increase in its area?
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Area of circle = πd²/4 with diameter " d " .
Diameter is increased by 15% .
So new diameter = d + 15/100d = d + 3/20d = 23/20d .
Increase in area = π/4 ( (23/20)²d²-d²) = π/4d²( 529/400 - 1 )
= πd²/4 ( 129/400)
Percentage of increase in area = πd²/4( 129/400) / πd²/4 * 100 = 129/400 * 100 = 129/4 = 32.25 % .
Diameter is increased by 15% .
So new diameter = d + 15/100d = d + 3/20d = 23/20d .
Increase in area = π/4 ( (23/20)²d²-d²) = π/4d²( 529/400 - 1 )
= πd²/4 ( 129/400)
Percentage of increase in area = πd²/4( 129/400) / πd²/4 * 100 = 129/400 * 100 = 129/4 = 32.25 % .
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