Objętość bryły wpisanej w sześcian

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); }}