Question

If the diameter of a sphere is decreased by 20% .By what percent does its curved surface area decrease?

Answer 1

let the diameter of sphere = d 
So that radius of sphere = d/2 
curved surface area        = 4πr² = 4π(d/2)² = 4πd²/4 = πd²
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20% of d = 20d/100 
New diameter = d - 20d/100
                       = 100d - 20d/100
                       = 80d/100
                       = 8d/10 = 4d/5

New radius     = 4d/10

New CSA       = 4π(4d/10)² = 4π (16d²/100) = 64πd²/100

difference between 1st CSA and 2nd CSA 

πd² - 64πd²/100

πd²(1-64/100)

πd²(100-64/100)

πd²(36/100)

36πd²/100

Amount of CSA decreased = 36d²/100

What percent of πd² is 36d²/100

Let p% of πd² is 36d²/100

pπd²/100 = 36d²/100

pπ x d²/100 = 36 x d²/100

pπ = 36 

p   = 36/π%

p  = 36 x 7/22 
    = 11.45 %