Question

the surface area of a solid sphere is increased by 21% without changing the shape find the percent of radius and volume

Answer 1

Solution:-
Let the original radius be 'r' and after changes the radius is 'R'
Now,
Surface Area of Sphere = 4πr²
4πr² = 100 (Original area)
4πR² = 121 (Area after increase of 21 %)
r²/R² = 100/121
r/R = 10/11
Now, increased value of radius in percentage.
11 - 10 = 1
= (1/10) × 100
= 10 %
So, radius will increase by 10 %

Now, Volume
Volume of Sphere = 4/3πr³
Ratio of volumes = 4/3πr³ : 4/3πR³
r³ : R³
(10)³ : (11)³
1000 : 1331
Increase in volume 
= 1331 - 1000
 = 331 
Now, increased value of volume in prcentage
(331/1000) ×100
= 33.1 %
So, the volume will be increased by 33.1 %
Answer.