From fc6aa4fb2988e741209d0564e8493ea10ab8927b Mon Sep 17 00:00:00 2001 From: Wang Weiye Date: Tue, 18 Oct 2022 17:50:00 +0800 Subject: [PATCH] 20221018 afternoon --- 题库0.3/Problems.json | 278 ++++++++++++++++++++++++++++++++++++++++-- 1 file changed, 268 insertions(+), 10 deletions(-) diff --git a/题库0.3/Problems.json b/题库0.3/Problems.json index 9a14602f..564a9fba 100644 --- a/题库0.3/Problems.json +++ b/题库0.3/Problems.json @@ -118019,7 +118019,7 @@ }, "004696": { "id": "004696", - "content": "如图, 在正方体$ABCD-A_1B_1C_1D_1$中, 点$MN$分别在棱$AA_1CC_1$上, 则``直线$MN\\perp\\text{直线}C_1B$''是``直线$MN\\perp\\text{平面}C_1BD$''的\\bracket{20}.\n\\begin{center}\n \\begin{tikzpicture}[scale = 0.6]\n \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (40:{2/2}) node [right] {$C$} coordinate (C)\n --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (220:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (40:{2/2}) (B1) --++ (-2,0);\n \\draw [dashed] (A) --++ (40:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n \\draw ($(A)!0.8!(A1)$) node [left] {$M$} coordinate (M);\n \\draw ($(C1)!0.8!(C)$) node [right] {$N$} coordinate (N);\n \\draw [dashed] (M) -- (N) (C1) -- (D) -- (B);\n \\draw (B) -- (C1);\n \\end{tikzpicture}\n\\end{center}\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既不充分又不必要条件}", + "content": "如图, 在正方体$ABCD-A_1B_1C_1D_1$中, 点$M,N$分别在棱$AA_1,CC_1$上, 则``直线$MN\\perp\\text{直线}C_1B$''是``直线$MN\\perp\\text{平面}C_1BD$''的\\bracket{20}.\n\\begin{center}\n \\begin{tikzpicture}[scale = 0.6]\n \\draw (0,0) node [below left] {$A$} coordinate (A) --++ (2,0) node [below right] {$B$} coordinate (B) --++ (40:{2/2}) node [right] {$C$} coordinate (C)\n --++ (0,2) node [above right] {$C_1$} coordinate (C1)\n --++ (-2,0) node [above left] {$D_1$} coordinate (D1) --++ (220:{2/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n \\draw (A) ++ (2,2) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (40:{2/2}) (B1) --++ (-2,0);\n \\draw [dashed] (A) --++ (40:{2/2}) node [left] {$D$} coordinate (D) --++ (2,0) (D) --++ (0,2);\n \\draw ($(A)!0.8!(A1)$) node [left] {$M$} coordinate (M);\n \\draw ($(C1)!0.8!(C)$) node [right] {$N$} coordinate (N);\n \\draw [dashed] (M) -- (N) (C1) -- (D) -- (B);\n \\draw (B) -- (C1);\n \\end{tikzpicture}\n\\end{center}\n\\twoch{充分非必要条件}{必要非充分条件}{充要条件}{既不充分又不必要条件}", "objs": [ "K0609003B", "K0611002B" @@ -220690,7 +220690,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030160" + ], "remark": "", "space": "12ex" }, @@ -220734,7 +220736,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030168" + ], "remark": "", "space": "12ex" }, @@ -220781,7 +220785,9 @@ "20220726\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030161" + ], "remark": "", "space": "12ex" }, @@ -224843,7 +224849,9 @@ "20221017\t周双" ], "same": [], - "related": [], + "related": [ + "030164" + ], "remark": "", "space": "12ex" }, @@ -224868,7 +224876,9 @@ "20221017\t周双" ], "same": [], - "related": [], + "related": [ + "030163" + ], "remark": "", "space": "12ex" }, @@ -232365,7 +232375,9 @@ "20220730\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030162" + ], "remark": "", "space": "12ex" }, @@ -250137,7 +250149,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030165" + ], "remark": "", "space": "12ex" }, @@ -250184,7 +250198,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030166" + ], "remark": "", "space": "12ex" }, @@ -250257,7 +250273,9 @@ "20220806\t王伟叶" ], "same": [], - "related": [], + "related": [ + "030167" + ], "remark": "", "space": "12ex" }, @@ -292400,5 +292418,245 @@ ], "remark": "", "space": "12ex" + }, + "030160": { + "id": "030160", + "content": "已知正三棱锥的底面边长是$2$, 高是$4$, 则该正三棱锥的表面积为\\blank{50}.", + "objs": [ + "K0620004B" + ], + "tags": [ + "第六单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "二期课改练习册高三-20221018修改", + "edit": [ + "20220726\t王伟叶", + "20221018\t周双" + ], + "same": [], + "related": [ + "009207" + ], + "remark": "", + "space": "" + }, + "030161": { + "id": "030161", + "content": "已知三棱柱的底面是$\\triangle ABC$, $AB=13\\text{cm}$, $BC=5\\text{cm}$, $CA=12\\text{cm}$, 侧棱$AA'$的长是$20\\text{cm}$, 且侧棱$AA'$与底面所成的角为$60^\\circ$, 则这个三棱柱的体积为\\blank{50}.", + "objs": [ + "K0616003B" + ], + "tags": [ + "第六单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "二期课改练习册高三-20221018修改", + "edit": [ + "20220726\t王伟叶", + "20221018\t周双" + ], + "same": [], + "related": [ + "009211" + ], + "remark": "", + "space": "" + }, + "030162": { + "id": "030162", + "content": "把一个半径为$R$的实心铁球熔化铸成两个小球, 两个小球的半径之比为$1:2$. 则其中较小球的半径为\\blank{50}.", + "objs": [ + "K0623002B" + ], + "tags": [ + "第六单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第三册课堂练习-20221018修改", + "edit": [ + "20220730\t王伟叶", + "20221018\t周双" + ], + "same": [], + "related": [ + "009731" + ], + "remark": "", + "space": "" + }, + "030163": { + "id": "030163", + "content": "已知圆锥的母线$l$与底面成$45^\\circ$角, 这个圆锥的体积为$9\\pi$, 则这个圆锥的高$h=$\\blank{50}, 侧面积为\\blank{50}.", + "objs": [ + "K0617006B", + "K0619003B" + ], + "tags": [ + "第六单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "二期课改练习册高三--20221017修改-20221018修改", + "edit": [ + "20220726\t王伟叶", + "20221017\t周双", + "20221018\t周双" + ], + "same": [], + "related": [ + "009400" + ], + "remark": "", + "space": "" + }, + "030164": { + "id": "030164", + "content": "在球内有相距$9$的两个平行的截面. 若两截面圆为球的小圆时, 其面积分别为$49\\pi$、$400\\pi$, 则此球的表面积为\\blank{50}, 体积为\\blank{50}.", + "objs": [ + "K0622005B", + "K0623002B", + "K0623004B" + ], + "tags": [ + "第六单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "二期课改练习册高三--20221017修改-20221018修改", + "edit": [ + "20220726\t王伟叶", + "20221017\t周双", + "20221018\t周双" + ], + "same": [], + "related": [ + "009399" + ], + "remark": "", + "space": "" + }, + "030165": { + "id": "030165", + "content": "已知圆锥底面的半径为$10$, 母线长为$60$. 则底面圆周上一点$B$沿侧面绕两周回到点$B$的最短距离为\\blank{50}.", + "objs": [ + "K0620005B" + ], + "tags": [ + "第六单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第三册习题-20221018修改", + "edit": [ + "20220806\t王伟叶", + "20221018\t周双" + ], + "same": [], + "related": [ + "010517" + ], + "remark": "", + "space": "" + }, + "030166": { + "id": "030166", + "content": "如图, 以正方体$ABCD-A_1B_1C_1D_1$六个面的中心为顶点所构成的多面体有多少条棱和多少个面? 设正方体的棱长为$1$, 则这个多面体的表面积为\\blank{50}, 体积为\\blank{50}.\n\\begin{center}\n\\begin{tikzpicture}[>=latex]\n\\draw (0,0) node [below left] {$A$} coordinate (A) --++ (3,0) node [below right] {$B$} coordinate (B) --++ (45:{3/2}) node [right] {$C$} coordinate (C)\n--++ (0,3) node [above right] {$C_1$} coordinate (C1)\n--++ (-3,0) node [above left] {$D_1$} coordinate (D1) --++ (225:{3/2}) node [left] {$A_1$} coordinate (A1) -- cycle;\n\\draw (A) ++ (3,3) node [right] {$B_1$} coordinate (B1) -- (B) (B1) --++ (45:{3/2}) (B1) --++ (-3,0);\n\\draw [dashed] (A) --++ (45:{3/2}) node [left] {$D$} coordinate (D) --++ (3,0) (D) --++ (0,3);\n\\draw ($(A)!0.5!(D1)$) coordinate (P);\n\\draw ($(B)!0.5!(A1)$) coordinate (Q);\n\\draw ($(C)!0.5!(B1)$) coordinate (R);\n\\draw ($(D)!0.5!(C1)$) coordinate (S);\n\\draw ($(A)!0.5!(C)$) coordinate (X);\n\\draw ($(A1)!0.5!(C1)$) coordinate (Y);\n\\draw [dashed] (P) -- (Q) -- (R) -- (S) -- (P);\n\\draw [dashed] (X) -- (P) -- (Y) (X) -- (Q) -- (Y) (X) -- (R) -- (Y) (X) -- (S) -- (Y);\n\\end{tikzpicture}\n\\end{center}", + "objs": [ + "K0619003B" + ], + "tags": [ + "第六单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第三册习题-20221018修改", + "edit": [ + "20220806\t王伟叶", + "20221018\t周双" + ], + "same": [], + "related": [ + "010519" + ], + "remark": "", + "space": "" + }, + "030167": { + "id": "030167", + "content": "一个直角三角形有一个$\\dfrac\\pi 6$的内角, 这个内角所对直角边的长度为$1$. 把这个三角形绕其斜边旋转一周, 则所得旋转体的表面积为\\blank{50}, 体积为\\blank{50}.", + "objs": [ + "K0616004B", + "K0617007B" + ], + "tags": [ + "第六单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "新教材必修第三册习题-20221018修改", + "edit": [ + "20220806\t王伟叶", + "20221018\t周双" + ], + "same": [], + "related": [ + "010522" + ], + "remark": "", + "space": "" + }, + "030168": { + "id": "030168", + "content": "已知侧面积为$27$的正三棱柱的侧棱恰好是某个圆柱的三条母线, 且这个圆柱的底面半径为$2$, 则这个圆柱的表面积为\\blank{50}.", + "objs": [ + "K0617006B" + ], + "tags": [ + "第六单元" + ], + "genre": "填空题", + "ans": "", + "solution": "", + "duration": -1, + "usages": [], + "origin": "二期课改练习册高三-20221018修改", + "edit": [ + "20220726\t王伟叶", + "20221018\t周双" + ], + "same": [], + "related": [ + "009209" + ], + "remark": "", + "space": "" } } \ No newline at end of file