Question

The diameter of a sphere is decreased by 25% By what per cent does its curved surface area decrease?

Answer 1

Let's say the the original diameter is 'd'. Now the diameter is decreased by 25% i.e. the new diameter dⁿ is d-25%d=(0.75)d. Formula for curved surface area S=Πd². Let the new surface area be Sⁿ=Π(dⁿ)². Take the ratio, Sⁿ:S=(dⁿ)²:d²= (3/4)². New surface area is Sⁿ=(9/16)S. Decrease in surface area is S-(9/16)S=(7/16)S. Percentage decrease in surface area is 43.75. Hence surface area decreases by 43.75%

Answer 2

so let the diameter of the sphere be d so radius = d/2 

so curved surface area = 4πd²/4 = πd² unit²

so the diameter is reduced by 25 % so new diameter = d x 75/100 = 3d/4 

so new radius = 3d/8  

so new surface area = 4. π. 9d²/64 = 9πd²/16 unit²

so the percentage difference = 9πd²/16/πd² x 100 = 9/16 x 100 = 225/4 = 56.25 %

so total decrease = 100 - 56.25 = 43.75 %