area of the bowl.
9: The radius of a sphere is decreased by 20 %. DJ
what per cent its curved surface area decreases ?
four spheres
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Let the diameter of sphere be "d"
surface area of sphere , S = 4πr²
= π (2r)²
= π(d)²
Diameter of sphere decreases by 20%
New diameter = d - (d/5) = [5d- d] / 5 = 4d/5
New surface area , S' = π(4d/5)²
= (16/25) πd²
Change in surface area of sphere = S - S'
= πd² – (16/25) πd²
= (9/25) πd²
Decrease in surface area = [(9/25πd²) / πd²] x 100 = 9 / 25 × 100 = 36 %
Therefore the decrease in S.A of sphere is 36%
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