20221018 afternoon
This commit is contained in:
parent
1926bcfd0a
commit
fc6aa4fb29
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@ -118019,7 +118019,7 @@
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},
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"004696": {
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"id": "004696",
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"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}",
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"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}",
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"objs": [
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@ -220690,7 +220690,9 @@
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"20220726\t王伟叶"
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"remark": "",
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"space": "12ex"
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},
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@ -220734,7 +220736,9 @@
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"20220726\t王伟叶"
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],
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"030168"
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"space": "12ex"
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@ -220781,7 +220785,9 @@
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"20220726\t王伟叶"
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],
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"same": [],
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"space": "12ex"
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},
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@ -224843,7 +224849,9 @@
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"20221017\t周双"
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],
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"space": "12ex"
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@ -224868,7 +224876,9 @@
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"20221017\t周双"
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],
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"same": [],
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"space": "12ex"
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@ -232365,7 +232375,9 @@
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"20220730\t王伟叶"
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],
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"same": [],
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@ -250137,7 +250149,9 @@
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"20220806\t王伟叶"
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],
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"same": [],
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@ -250184,7 +250198,9 @@
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"20220806\t王伟叶"
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],
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"same": [],
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"related": [],
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"030166"
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"space": "12ex"
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@ -250257,7 +250273,9 @@
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"20220806\t王伟叶"
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],
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"same": [],
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"related": [],
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"related": [
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"030167"
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"remark": "",
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"space": "12ex"
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@ -292400,5 +292418,245 @@
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],
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"remark": "",
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"space": "12ex"
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},
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"030160": {
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"id": "030160",
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"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}.",
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"objs": [
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"K0620004B"
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],
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"tags": [
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"第六单元"
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],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "二期课改练习册高三-20221018修改",
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"edit": [
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"20220726\t王伟叶",
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"20221018\t周双"
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],
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"same": [],
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"related": [
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"009207"
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],
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"remark": "",
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"space": ""
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},
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"030161": {
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"id": "030161",
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"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}.",
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"objs": [
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"K0616003B"
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],
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"tags": [
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"第六单元"
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],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "二期课改练习册高三-20221018修改",
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"edit": [
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"20220726\t王伟叶",
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"20221018\t周双"
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],
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"same": [],
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"related": [
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"009211"
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"remark": "",
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"space": ""
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},
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"030162": {
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"id": "030162",
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"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}.",
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"objs": [
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"K0623002B"
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],
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"tags": [
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"第六单元"
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],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "新教材必修第三册课堂练习-20221018修改",
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"edit": [
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"20220730\t王伟叶",
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"20221018\t周双"
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],
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"same": [],
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"related": [
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"009731"
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],
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"remark": "",
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"space": ""
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},
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"030163": {
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"id": "030163",
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"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}.",
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"objs": [
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"K0617006B",
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"K0619003B"
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],
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"tags": [
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"第六单元"
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],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "二期课改练习册高三--20221017修改-20221018修改",
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"edit": [
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"20220726\t王伟叶",
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"20221017\t周双",
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"20221018\t周双"
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],
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"same": [],
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"related": [
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"009400"
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],
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"remark": "",
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"space": ""
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},
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"030164": {
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"id": "030164",
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"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}.",
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"objs": [
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"K0622005B",
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"K0623002B",
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"K0623004B"
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],
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"tags": [
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"第六单元"
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],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "二期课改练习册高三--20221017修改-20221018修改",
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"edit": [
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"20220726\t王伟叶",
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"20221017\t周双",
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"20221018\t周双"
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],
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"same": [],
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"related": [
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"009399"
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],
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"remark": "",
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"space": ""
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},
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"030165": {
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"id": "030165",
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"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}.",
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"objs": [
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"K0620005B"
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],
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"tags": [
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"第六单元"
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],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "新教材必修第三册习题-20221018修改",
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"edit": [
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"20220806\t王伟叶",
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"20221018\t周双"
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],
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"same": [],
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"related": [
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"010517"
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],
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"remark": "",
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"space": ""
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},
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"030166": {
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"id": "030166",
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"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}",
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"objs": [
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"K0619003B"
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],
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"tags": [
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"第六单元"
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],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "新教材必修第三册习题-20221018修改",
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"edit": [
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"20220806\t王伟叶",
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"20221018\t周双"
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],
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"same": [],
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"related": [
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"010519"
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],
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"remark": "",
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"space": ""
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},
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"030167": {
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"id": "030167",
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"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}.",
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"objs": [
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"K0616004B",
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"K0617007B"
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],
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"tags": [
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"第六单元"
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],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "新教材必修第三册习题-20221018修改",
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"edit": [
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"20220806\t王伟叶",
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"20221018\t周双"
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],
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"same": [],
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"related": [
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"010522"
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],
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"remark": "",
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"space": ""
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},
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"030168": {
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"id": "030168",
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"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}.",
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"objs": [
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"K0617006B"
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],
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"tags": [
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"第六单元"
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],
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"genre": "填空题",
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"ans": "",
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"solution": "",
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"duration": -1,
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"usages": [],
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"origin": "二期课改练习册高三-20221018修改",
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"edit": [
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"20220726\t王伟叶",
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"20221018\t周双"
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],
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"same": [],
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"related": [
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"009209"
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"remark": "",
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"space": ""
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}
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}
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