题目内容
(本小题满分8分)
已知直四棱柱的底面是边长为a的正方形, 高为, 体积为V, 表面积等于S.
(1) 当a =" 2," h = 3时,分别求V和S;
(2) 当V = 12,S = 32时,求的值.
已知直四棱柱的底面是边长为a的正方形, 高为, 体积为V, 表面积等于S.
(1) 当a =" 2," h = 3时,分别求V和S;
(2) 当V = 12,S = 32时,求的值.
(1)32
(2)
(1) 当a =" 2," h = 3时,
V =" " a2h=" 12" ;
S =" 2a2+" 4ah ="32 " . --- 4分
(2) ∵a2h=" 12," 2a(a + 2h) =32,
∴ , (a + 2h) =,
∴===. --- 4分
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