If the diameter of a sphere is decreased by 25% by what percent does its curved surface area decrease?

Detailed solution can be understood by knowing the formula of csa and also the percentage calculations.
Concept- The formula for determining the curved surface area (CSA) of a sphere is
 C.S.A = 4πr2.
C.S.A = The sum of areas of all the faces of a 3D object is called as  Let us assume the diameter of the sphere is “d”.
So, the radius of the sphere in form of diameter is as given:
r = $\frac{d}{2}$
The C.S.A. of  the sphere = 4πr2 =  4π${\left(\frac{d}{2}\right)}^2$
Therefore, the C.S.A of the sphere = πd2
Decrease percentage in diameter = 25%
⇒ 25% of d = d $\times$ $\frac{25}{100}$ = $\frac{d}{4}$
 ⇒  $\frac{d}{4}$ will be subtracted from total diameter (d).
So, the new diameter will be  D = d - $\frac{d}{4}$ = $\frac{3d}{4}$
Hence, the new curved surface area of the sphere = πD2
⇒ π${\left(\frac{3d}{4}\right)}^2$
⇒ $\frac{9\pi d^2}{16}$
Percentage decrease in the C.S.A  = $\frac{\pi d^2 -\mathit{ \pi }{D}^2}{\pi d^2}$ $\times$ 100
 ⇒ $\frac{\pi d^2 -\mathit{ \pi }{D}^2}{\pi d^2}$ $\times$ 100
 ⇒ $\frac{1 - \frac{9}{16}}{1}$  $\times$ 100
⇒ $\frac{7}{16}$  $\times$ 100
⇒ 43.75%
Hence, the correct option is 1.