如图，正方体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)的棱长为\(2\)，\(E\)，\(F\)分别是\(CB\)，\(CD\)的中点，点\(M\)在棱\(CC_{1}\)上，\(CM=tCC_{1}(0 < t < 1)\)．\((\)Ⅰ\()\)三棱锥\(C-EFM\)，\(C_{1}-B_{1}D_{1}M\)的体积分别为\(V_{1}\)，\(V_{2}\)，当\(t\)为何值时，\(V_{1}⋅V_{2}\)最大？最大值为多少？ \((\)Ⅱ\()\)若\(A_{1}C/\!/\)平面\(B_{1}D_{1}M\)，证明：平面\(EFM⊥\)平面\(B_{1}D

如图，正方体\(ABCD-A_{1}B_{1}C_{1}D_{1}\)的棱长为\(2\)，\(E\)，\(F\)分别是\(CB\)，\(CD\)的中点，点\(M\)在棱\(CC_{1}\)上，\(CM=tCC_{1}(0 < t < 1)\)．
\((\)Ⅰ\()\)三棱锥\(C-EFM\)，\(C_{1}-B_{1}D_{1}M\)的体积分别为\(V_{1}\)，\(V_{2}\)，当\(t\)为何值时，\(V_{1}⋅V_{2}\)最大？最大值为多少？
\((\)Ⅱ\()\)若\(A_{1}C/\!/\)平面\(B_{1}D_{1}M\)，证明：平面\(EFM⊥\)平面\(B_{1}D_{1}M.\)

【考点】面面垂直的判定,圆柱、圆锥、圆台的侧面积、表面积和体积

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难度：较易

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