The diameter of a sphere is decreased by 25%. -Maths 9th

The diameter of a sphere is decreased by 25%. -Maths 9th
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Let the original diameter of the sphere be 2x.  Then, original radius of the sphere = x  Original curved surface area = 4πr2  Decreased diameter of the sphere = 2x - 25% of 2x = 2x - x/2 = 3/2x Decreased radius of the sphere = 3/4x  ∴  Decreased curved surface area = 4 π(3/4.x)2 = 9/4πx2 Decrease in area = 4 πx2 - 9/4πx2 = 7/4πx2  Hence, percentage decreases in area =   7/4πx2/4πx2 x 100% = 7/16 x 100% = 175/4% = 43.75%
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