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