S(осн)=a^2sqrt(3)/4
S(бок)=3*S(осн)
S(полн)=4(a^2*(sqrt(3)/4)
4a^2sqrt(3)/4=324sqrt(3)
a^2=324
a=18 см
H^2=a^2-R^2=a^2-(asqrt(3)/3)^2=a^2-(a^2/3)=2a^2/3
H=a*sqrt(2/3)
V=(1/3)*S(осн)*H
V=(1/3)*324*(sqrt(3)/4)*18sqrt(2/3)=486sqrt(2) см^3
О т в е т. 486 см^3