Question

if the radius of a spherical ball increased by 5% what is the percentage increase in its volume?

Answer 1

Volume of a sphere :

V = ( 4 \ 3 ) * pi * r ^ 3


Radius increased by 5%

New radius :

rN = r + ( 5 / 100 ) * r = r + 0.05 * r = 1.05 * r

rN = 1.05 * r


New volume of a sphere :

VN = { 4 \ 3 ) * pi * rN ^ 3 =

{ 4 \ 3 ) * pi * ( 1.05 r ) ^ 3 =

{ 4 \ 3 ) * pi * ( 1.05 ) ^ 3 * r ^ 3 =

{ 4 \ 3 ) * pi * r ^ 3 * ( 1.05 ) ^ 3 =

V * ( 1.05 ) ^ 3 =

V * 1.157625 =

1.157625 * V =

V + 0.157625 * V


0.157625 = 0.157625 * 1 = 0.157625 * 100 / 100 =

15.7625 / 100 =

15.7625 %


Volume of a sphere increased by 15.7625 %