Question

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

Answer 1

let first radius=r
let second radius=R
A/Q
r+10%of r=R
r+10/100*r=R
11r/10=R


volume1=4/3πr^3 ---------①
volume2=4/3πR^3---------②
①/②
volume1/volume2=(4/3πr^3)/(4/3πR^3)
volume1/volume2=r^3/R^3
volume1/volume2=r*r*r/R*R*R
volume1/volume2=r*r*r/((11r/10)*(11r/10)*(11r/10))
volume1/volume2=1000/1331
1331volume1=1000volume2
1331volume1/1000=volume2


increase in volume =volume2-volume1/volume1*100
=(((1331volume1/1000)-volume1))/volume1)*100
=(331volume1/1000)/volume1*100
=33.1%ans......