P_b=60\pi=2\pi rH
P_c=78\pi=2\pi r(r+H)
V=\pi r^2H
2\pi rH=60\pi
r=\frac{60}{2H}
2\pi r(r+H)=78\pi
2*\frac{60}{2H}(\frac{60}{2H}+H)=78
\frac{60}{H}(\frac{60}{2H}+H)=78
60(\frac{60}{2H}+H)=78H
\frac{3600}{2H}+60H=78H
3600+120H^2=156H^2
36H^2=3600
H^2=100
H=10
r=\frac{60}{2H}=\frac{60}{2*10}=\frac{60}{20}=3
V=\pi r^2H=3^2*10 \pi=90 \pi cm^3