Question

5. If the diameter of a sphere is decreased by 25% then by what percentage does it curved surface area will decrease?​ (plz explain step by step)

Answer 1

Answer:

43.75%

Step-by-step explanation:

D= diameter R= d/2

The curved area is ( A= 4$\pi$r= which is nothing but 4$\pi$d/2= $\pi$d square.

so according to the question the diameter is increased by 25% = 75/100 * d= 3d/ 4.

new surface area= 4$\pi$r square=  4$\pi$( 3d/ 2.4) square 9/16$\pi d^{2}$

decrease in surface area= $\pi d^{2}$ - $9/16\pi d^{2}$ = $7/16\pi d^{2}$

So the  %  decrease in Surface Area= Decrease in surface area / Surface area × 100%

$7\pi d^{2} / 16\pi d^{2}$ * 100 = 7/16 * 100= 43.75%