円柱を切断した部分の体積 - KeTCindyによる図入り教材の作成

切断した図を描く

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setudan.zip

Spaceline("1",[-X3d,X3d]);
Expr([sl2d1_1,"e","x"]);
／／　x軸を描く
fd1=[
"p",
"x=3*cos(T)","y=3*sin(T)","z=u*3*sin(T)",
"u=[0,1]","T=[0,pi]"," "
];
／／　側面の３dデータ
Sfbdparadata("1",fd1,["Wait=10"],[]);
／／　輪郭線を取得
Spacecurve("1","3*[cos(t),sin(t),sin(t)]","t=[0,pi]");
Spacecurve("2","3*[cos(t),sin(t),0]","t=[0,pi]",["nodisp"]);
／／　底面と上面の３d曲線
tmp=Intersectcrvs("sc2d2","sfbd2d1",[0.01]);
Partcrv("1",tmp_1,sc2d2_length(sc2d2),"sc2d2",["do"]);
Partcrv("2",sc2d2_1,tmp_1,"sc2d2");
／／　側面との交点以下を点線で描く
Putpoint3d(["A",[-1.8,0,0]],"fix");
Spaceline("3",[A3d,A3d+[0,4,0]],["nodisp"]);
Putintersect("B","sl2d3","sc2d2");
Spaceline("4",[B3d,B3d+[0,0,4]],["nodisp"]);
Putintersect("C","sl2d4","sc2d1");
Listplot("1",[A,B,C],["do"]);
Listplot("2",[C,A]);
Spaceline("5",[O3d,O3d+[0,4,0]],["nodisp"]);
Putintersect("D","sl2d5","sc2d2");
Spaceline("6",[D3d,D3d+[0,0,4]],["nodisp"]);
Putintersect("E","sl2d6","sc2d1");
Listplot("3",[O,D,E],["do"]);
Fontsize("s");
Letter([Parapt([3,0,0]),"se","A",Parapt([-3,0,0]),"se","B"]);
Letter([Parapt([0,0,0]),"se","O"]);
Expr([A,"se","x"]);
Expr([(D+E)/2,"w","r",(O+D)/2,"sw","r"]);
Expr([(A+B)/2,"sw","\sqrt{r^2-x^2}",(B+C)/2,"sw","\sqrt{r^2-x^2}"]);