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== 問題以上,答以下 ==

• 文章題では,問題をじっくり読むことが大切です.
• ここでは答を気にせずに,問題を読むことに集中しましょう.

《もとの問題》
 右の図のように,AB=4cm,BC=2cmの長方形ABCDがある.平面上でこの長方形を頂点Cを中心に90だけ時計回りに回転させたとき,次の問い(1)(2)に答えよ.
(1)
 辺ABが描く図形として,正しいものはどれか.下の略図(ア)~(オ)から選べ.
(ア)
(イ)
(ウ)
(エ)
(オ)
(2)
 (1)で辺ABの描いた図形の面積を求めよ.
(「京都府 平成11年度」問題の引用)



《答える前に》
(1)(2)では「何が」描いた図形について,質問しているのですか.
(正しいものを選びなさい↓)
長方形ABCD, 辺AB, 点Aと点B
 点Cを中心として,CA,CB,CDを半径とする円を描くと,点A,B,Dの動いたあとは右図のようになります.上の問題(1)で「点Aと点B」の動いたあとが「両方とも」正しく描かれている図はどれですか.
(正しいものを選びなさい↓)
(ア) (イ) (ウ) (エ) (オ)
 

さて,ちょうど半径になっているものを,右図のようにxだけ回転したとき,この半径が動いたあとは,扇形になります.
 半径がrの扇形の図形の面積は,中心角に比例します.中心角xの扇形の面積をS,中心角360の円の面積πr2を用いると,S:πr2=x:360 です.これを変形して,Sをπ,r,xで表わすと,(正しいものを選びなさい↓)
 xが90のときは,
(正しいものを選びなさい↓)
,

上の問題(2)のように,半径以外のものを回転させたとき,動いたあとにできる図形は
A
のように,凹凸を埋めると「扇形」や「中抜きの扇形」になります.
 上の例Aにおいて,円の半径が2√5で回転角が90のとき,L字形の動いたあとにできる図形の面積は(正しいものを選びなさい↓)
4π, 5π, √5π, 20π
 上の例Bにおいて,外の円の半径が2√5,中の円の半径が2で回転角が90のとき,線分の動いたあとにできる図形の面積は(正しいものを選びなさい↓)
π, 4π, 5π, √5π, 16π


《類題》
 右の図のように,△OABがあり,O(0,0),A(6,0),B(8,4)とする.このとき,次の問い(1)(2)に答えよ.
(1)
 平面上で三角形OABを点Oを中心に90時計回りに回転させたとき,辺ABが描く図形として正しいものはどれか.下の略図(ア)~(エ)から選べ.
(ア)
(イ)
(ウ)
(エ)
(2)
 (1)で辺ABの描いた図形の面積を求めよ.ただし,円周率はπとする.
(「京都府 平成7年度」問題の引用)
(正しいものを選びなさい↓)
(1)
(ア) (イ) (ウ) (エ)

(2)
9π, 11π, 20π, 80π


《類題》
 右の図のように,長さ4cmの線分ABがあり,その中点Mで円Oに接している.
 このとき,次の問い(1)(2)に答えよ.
(1)
 線分ABが,中点Mで円に接しながら,円Oのまわりを1周したとき,線分ABの描く図形として正しいものはどれか,下の略図(ア)~(エ)から選べ.
(ア)
(イ)
(ウ)
(エ)
(2)
 (1)で線分ABの描いた図形の面積を求めよ.ただし,円周率はπとする.
(「京都府 平成9年度」問題の引用)
《答える前に》
(正しいものを選びなさい↓)
(1)
(ア) (イ) (ウ) (エ)
(2)
 円Oの半径はいくらですか.(正しいものを選びなさい↓)
, , √3, , 書いてない

 下の2つの図で黄色で示したドーナツ状の図形の面積が,円Oの半径rに無関係に一定になるという性質があれば,(2)の問題が解けるはずです.
 下の図(どちらでも)において,外側に描かれた円の半径をrを用いて表わすと,どうなりますか.(正しいものを選びなさい↓)

, , , , , , 
 上の図で黄色で示したドーナツ状の図形(1つ)の面積は,いくらですか.
(正しいものを選びなさい↓)
2π, 3π, 4π
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