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

Question

The diameter of a sphere is decreased by 25%. By what per cent does it&#x2019;s curved surface area decrease?

Philoid · Accepted Answer

Let the diameter be d

Radius (r1) =

New radius (r2) = (1 - )

= d

CSA (S1) = 4r1²

= 4π ()²

= πd²

CSA (S2) = 4πr2²

= 4π ()²

= d²

Decrease in surface area = S1 – S2

= πd² - d²

= πd²

Now,

Percentage decrease = * 100

= * 100

=

= 43.75 %