Question

If the radius of a circle is increased by 10 % then prove the volume will increase by 33.1%

Answer 1

so
if increase by 10%, that means times 1.1

sub 1.1r for r in
V=(4/3)pir³

so
nV=(4/3)pir³
nV=(4/3)pi(1.1r)³
nV=(4/3)pi1.331r³
nv=((4/3)pir³)1.331

V=(4/3)pir³

nV=(V)1.331

x times 1.331 is about a 33% increase