Question

the diameter of a sphere is decreased by 25%.by what per cent does its CSA decrease?​

Answer 1

Step-by-step explanation:

If diameter decreased by 25%

If diameter decreased by 25%Then new r=25/2%

If diameter decreased by 25%Then new r=25/2% CSA earlier was 4×pie×r²

If diameter decreased by 25%Then new r=25/2% CSA earlier was 4×pie×r²Now it is 4×pie×new r²

If diameter decreased by 25%Then new r=25/2% CSA earlier was 4×pie×r²Now it is 4×pie×new r²If we reduce the diameter by 25%, the radius will also be reduced by 25%.

let initial radius of sphere = r

initial CSA = 4πr²

after reducing it 25%,

25% of r = (25/100)×r = 0.25r

final radius = r - 0.25r = 0.75r

final CSA = 4π(0.75r²) = 4πr²×(0.5625)

decrease in CSA = initial CSA - final CSA = 4πr²

-  4πr² × (0.5625)

⇒decrease in CSA = 4πr² × (1-0.5625) = 4πr² × 0.4375

% decrease in CSA = 

Thus CSA decreases by 43.75%.