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展開図
立体を、平面に展開した図を、展開図（てんかいず）と呼ぶ。
\begin{xy}
(0,16)*{立方体}="A",
{(0,0) \ar @{-}(9,6)},
{(0,0) \ar @{-}(0,-9)},
{(0,0) \ar @{-}(-9,6)},
{(0,12) \ar @{-}(9,6)},
{(0,12) \ar @{-}(-9,6)},
{(9,6) \ar @{-}(9,-3)},
{(-9,6) \ar @{-}(-9,-3)},
{(0,-9) \ar @{-}(9,-3)},
{(0,-9) \ar @{-}(-9,-3)},
{(0,3) \ar @{.}(9,-3)},
{(0,3) \ar @{.}(-9,-3)},
{(0,3) \ar @{.}(0,12)},
\end{xy}
\begin{xy}
(5,36)*{立方体の展開図}="A",
(5,30)*{正方形が６枚}="A",
{(0,-12) \ar @{-}(0,24)},
{(-12,0) \ar @{-}(36,0)},
{(12,-12) \ar @{-}(12,24)},
{(-12,12) \ar @{-}(36,12)},
{(0,24) \ar @{-}(12,24)},
{(0,-12) \ar @{-}(12,-12)},
{(-12,0) \ar @{-}(-12,12)},
{(24,0) \ar @{-}(24,12)},
{(36,0) \ar @{-}(36,12)},
\end{xy}
\begin{xy}
(10,30)*{円柱}="A",
{(0,0) \ar @{-}(0,20)},
{(20,0) \ar @{-}(20,20)},
(0,-2)*+[o]{}="A";(20,-2)*+{}="B",
"A";"B" **\crv{~**@{.} (0,3)&(10,6)&(20,3)};
(0,2)*+[o]{}="A";(20,2)*+{}="B",
"A";"B" **\crv{~**@{-} (0,-3)&(10,-6)&(20,-3)};
(0,18)*+[o]{}="A";(20,18)*+{}="B",
"A";"B" **\crv{~**@{-} (0,23)&(10,26)&(20,23)};
(0,22)*+[o]{}="A";(20,22)*+{}="B",
"A";"B" **\crv{~**@{-} (0,17)&(10,14)&(20,17)};
\end{xy}
\begin{xy}
(15,51)*{円柱の展開図}="A",
(15,45)*{円が２枚＋４角形}="A",
{(0,0) \ar @{-}(0,20)},
{(40,0) \ar @{-}(40,20)},
{(0,0) \ar @{-}(40,0)},
{(0,20) \ar @{-}(40,20)},
(10,30) *\cir<10mm>{},
(10,-10) *\cir<10mm>{},
\end{xy}
＜例題 \( \Large 1 \) ＞ 以下の３角柱の、展開図を書きなさい。
\begin{xy}
(0,25)*{３角柱}="A",
{(0,6) \ar @{.}(-6,0)},
{(0,6) \ar @{.}(6,0)},
{(6,0) \ar @{-}(-6,0)},
{(0,21) \ar @{-}(-6,15)},
{(0,21) \ar @{-}(6,15)},
{(6,15) \ar @{-}(-6,15)},
{(0,6) \ar @{.}(0,21)},
{(6,0) \ar @{-}(6,15)},
{(-6,0) \ar @{-}(-6,15)},
\end{xy}
円錐の展開図
\begin{xy}
(10,24)*{円錐}="A",
{(0,0) \ar @{-}(10,15)},
{(20,0) \ar @{-}(10,15)},
(10,15)*{\bullet}="A",
(20,0)*{\bullet}="A",
(10,19)*{A}="A",
(21,4)*{B}="A",
(0,-2)*+[o]{}="A";(20,-2)*+{}="B",
"A";"B" **\crv{~**@{.} (0,1)&(10,4)&(20,1)};
(0,2)*+[o]{}="A";(20,2)*+{}="B",
"A";"B" **\crv{~**@{-} (0,-3)&(10,-5)&(20,-3)};
(10,-10)*{ABを母線と呼ぶ}="A",
\end{xy}
\begin{xy}
(15,16)*{円錐の展開図}="A",
(15,10)*{円＋扇形}="A",
(15,0) *\cir<15mm>{dl_ul},
(15,0)*{\bullet}="A",
{(15,0) \ar @{-}(26,-11)},
(26,-11)*{\bullet}="A",
{(15,0) \ar @{-}(4,-11)},
(4,-11)*{\bullet}="A",
(15,4)*{A}="A",
(29,-11)*{B}="A",
(0,-11)*{B}="A",
(15,-25) *\cir<10mm>{},
\end{xy}
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