Question

if the diameter of a sphere is decreased by 25% then by what percent its curved area would decrease plz answer me

Answer 1

Let the diameter of the sphere be d ⇒ radius = d/2 

 

So, curved surface area = 4πd²/4 = πd² unit²

 

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

 

⇒ new radius = 3d/8  

 

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

 

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

 

∴ total decrease = 100 - 56.25 = 43.75 %

You don’t need to know the formula for the volume of a sphere. All you need to know is that volume is proportional to diameter cubed.

So if the diameter is 25% less (ie. 0.75 times the original), then its new volume will be 0.75×0.75×0.75 times the original. Or 0.421875.

That number is 57.8125% less than the original.

Hope This Helps :)