Project ID:
6000000080
Accepted:
Typ:
Layout:
Question:
Wskaż objętość bryły (kula, walec, stożek i ostrosłup) wpisanej w sześcian o krawędzi równej $6\,\mathrm{cm}$ (spójrz na rysunek).
Question 1:
{\obrA}
Question 1 Image:
Answer 1:
$V=36\pi\,\mathrm{cm}^3$
Question 2:
{\obrB}
Question 2 Image:
Answer 2:
$V=54\pi\,\mathrm{cm}^3$
Question 3:
{\obrC}
Question 3 Image:
Answer 3:
$V=18\pi\,\mathrm{cm}^3$
Question 4:
{\obrD}
Question 4 Image:
Answer 4:
$V=72\,\mathrm{cm}^3$
Answer 5:
$V=96\,\mathrm{cm}^3$
Answer 6:
$V=72\pi\,\mathrm{cm}^3$
Tex:
% tiket 33413
\NastavOD{3}
\def\krychle#1{
\begin{tikzpicture}[z={(-0.8,-0.6)},x=3cm,y=3cm]
#1
\color{black}
\draw (0.5,1,0.5) coordinate (S);
\foreach \xx/\yy/\zz/\name/\pozice in {
0/0/0/D/left, 1/0/0/C/right, 1/1/0/G/above right, 0/1/0/H/above right,
0/0/1/A/below left, 1/0/1/B/below right, 1/1/1/F/right, 0/1/1/E/above left}
\draw (\xx,\yy,\zz) coordinate (\name);
\foreach \x/\y in {A/D, D/H, D/C} {\draw[dashed] (\x) -- (\y);}
\color{black}
\foreach \xx/\yy/\zz/\name/\pozice in {
0/0/0/D/left, 1/0/0/C/right, 1/1/0/G/above right, 0/1/0/H/above right,
0/0/1/A/below left, 1/0/1/B/below right, 1/1/1/F/right, 0/1/1/E/above left}
\draw (\xx,\yy,\zz);
\foreach \x/\y in {A/D, D/H, D/C} {\draw[dashed] (\x) -- (\y);}
\draw (A) -- (B) -- (F) -- (E) -- cycle;
\foreach \x/\y in {E/H, F/G, B/C, H/G, G/C} {\draw (\x) -- (\y);}
\end{tikzpicture}
}
\def\obrA{\krychle{
\begin{scope}[canvas is xz plane at y=0.5]
\draw [dashed, blue, thick] (0,0.5) arc (180:360:0.5);
\end{scope}
\begin{scope}[canvas is xz plane at y=0.5]
\draw [blue, thick] (1,0.5) arc (0:180:0.5);
\end{scope}
\begin{scope}[canvas is xy plane at z=.5]
\draw[blue, thick] (0.5,0.5) circle (0.515);
\end{scope}
}}
\def\obrB{\krychle{
\begin{scope}[canvas is xz plane at y=0]
\draw [dashed, blue, thick] (0,0.5) arc (180:360:0.5);
\end{scope}
\begin{scope}[canvas is xz plane at y=0]
\draw [blue, thick] (1,0.5) arc (0:180:0.5);
\end{scope}
\begin{scope}[canvas is xz plane at y=1]
\draw[blue, thick] (0.5,0.5) circle (0.5);
\end{scope}
\draw[blue, thick, shift={(1.2pt,2pt)}] (1,0,0.5)--(1,1,0.5);
\draw[blue, thick , shift={(-1.2pt,-2pt)}] (0,0,0.5)--(0,1,0.5);
}}
\def\obrC{\krychle{
\begin{scope}[canvas is xz plane at y=0]
\draw [dashed, blue, thick] (0,0.5) arc (180:360:0.5);
\end{scope}
\begin{scope}[canvas is xz plane at y=0]
\draw [blue, thick] (1,0.5) arc (0:180:0.5);
\end{scope}
\draw[blue,dashed, thick] (E)--(G);
\draw[blue,dashed, thick] (H)--(F);
\draw[blue, thick] (S)--(0,0,0.5);
\draw[blue, thick] (S)--(1.0,0,0.42);
}}
\def\obrD{\krychle{
\draw[blue,dashed, thick] (E)--(G);
\draw[blue,dashed, thick] (H)--(F);
\draw[blue, thick, dashed] (C)--(D)--(A);
\draw[blue, thick, dashed] (S)--(D);
\draw[blue, thick] (S)--(C);
\draw[blue, thick] (S)--(B);
\draw[blue, thick] (S)--(A);
\draw[blue, thick] (A)--(B)--(C);
}}