Question

The diameter of a sphere is decreased by 20%. By what percent does its curved surface area increase or decrease?​

Answer 1

Answer:

it will decrease it is very simple bro

Answer 2

Let the diameter of sphere be "d"

Curved surface area of sphere = 4πr²

 = π(2r)²

 = πd²

Given diameter of sphere decreases by 20%

New diameter =d − ($\frac{d}{5}$) = $\bold{\frac{4d}{5}}$

​New curved surface area =π$(\frac{4d}{5})^{2}$ = $\bold{\frac{16}{25}}$ πd²  

Change in surface area of sphere

=πd²  – ($\frac{16}{25}$ )πd²  = ($\bold{\frac{9}{25}}$ )πd²

 

Decrease in curved surface area

= $\sf{\frac{\frac{9}{25} \pi d^{2}}{\pi d^{2}} }$ × 100 = 36%

∴ Surface area decreases by 36%