V(cylinder)= πr²h
d=2r,
d is diameter, r is radius.
When diameter is tripled, a new diameter D=3d,
new radius R=3d/2=(3*2r)/2=3r
R=3r
V(new cylinder)= πR²h = π(3r)²h=9πr²h
V(new cylinder)/V(cylinder)=9πr²h/πr²h=9
Volume new cylinder 9 times more the volume of old cylinder.