在棱长为a的正方体ABCD-A1B1C1D1中,P、Q是对角线A1C上的点,若PQ=a/2,则三棱锥P-BDQ的体积为

A1C=√3a,PQ=a/2,
PQ=√3/6A1C,
BC⊥平面ABB1A1,A1B∈平面ABB1A1,
BC⊥A1B,A1B=√2a,
S△A1BC=√2a^2/2,
S△PQB=S△A1BC*(√3/6)=√6a^2/12,
V三棱锥A1-BDC=S△BDC*AA1/3=(a^2/2)*a/3=a^3/6,
设D至平面A1BC距离为h,
V三棱锥D-A1BC=S△A1BC*h/3=(√2a^2/2)h/3=√2ha^2/6,
V三棱锥A1-BDC=V三棱锥D-A1BC,
a^3/6=√2ha^2/6,
h=√2a/2,
∴VP-BDQ=S△BPQ*h/3
=(√6a^2/12)*(√2a/2)/3
=√3a^3/36.