Question

The radius of a sphere is increased by 10%. Prove that the volume will be increased by 33.1% approximately

Answer 1

yes..................

Answer 2

Let the radius of the sphere be r.

Therefore the volume of the sphere =

4/3πr*3...
Now the sphere is increased by 10%
=>new radius =10/100×r =>r/10.

Now new radius=r/10+r = 11r/10

New volume =4/3π(11r/10)*3
=4/3π1331r*3/1000

Increased volume =>4/3π1331r*3/1000-4/3πr*3

LCM =3000

Increased volume => 4/3π×331r*3/1000

Percentage of volume increased =>
4/3π331r*3/1000×100/(4/3πr*3)=>33.1%