Question

已知球面上有A、B、C、D四點,AB=1,BC=3,AC=,BD=,且BD⊥平面ABC,則此球的體積為____________.

Answer 1

4π  如圖,在△ABC中,AB=1,BC=3,AC=,

∴cosB==×3=.∴B=60°, =2r.

BD²+4r²=4R²,∴R=.∴V_球=π()³=4π.