Project ID:
6000000014
Accepted:
Tipo:
Layout:
Question:
Empareja la parte coloreada del disco con su área.
Question 1 Image:
Answer 1:
$\frac 83\pi \,\mathrm {cm}^2$
Question 2 Image:
Answer 2:
$4\sqrt 3\,\mathrm {cm}^2$
Question 3 Image:
Answer 3:
$\frac {8\pi -12\sqrt 3}3\,\mathrm {cm}^2$
Question 4 Image:
Answer 4:
$16\pi \,\mathrm {cm}^2$
Question 5 Image:
Answer 5:
$7\pi \,\mathrm {cm}^2$
Question 6 Image:
Answer 6:
$\frac 76\pi \,\mathrm {cm}^2$
Tex:
% tiket 32500
%%%%%%%%%%%
\NastavOT[-2pt]{3}
\def\preAnswers{\vspace*{-12pt}}
\def\preQuestions{\vspace*{-12pt}}
\otazka{\obrA}{$\frac83\pi\,\mathrm{cm}^2$}
\otazka{\obrB}{$4\sqrt3\,\mathrm{cm}^2$}
\otazka{\obrC}{$\frac{8\pi-12\sqrt3}3\,\mathrm{cm}^2$}
\otazka{\obrD}{$16\pi\,\mathrm{cm}^2$}
\otazka{\obrE}{$7\pi\,\mathrm{cm}^2$}
\otazka{\obrF}{$\frac76\pi\,\mathrm{cm}^2$}
\def\delka{0.75cm}
\def\obrA{
\obrMsr[x=\delka,y=\delka]{-6.5}{6.5}{-5.5}{5.5}
{
\coordinate (A) at (20:2);
\coordinate (B) at (80:2);
\coordinate (S) at (0,0);
\fill[vypln1] (A) arc (20:80:2) -- (S) -- cycle;
\draw[thick] (0,0) circle (2);
\draw[thick] (A) -- (S) -- node [sloped,above,xshift=-4pt]{$\scriptstyle{r=4\,\mathrm{cm}}$} (B);
\fill (S) node[below left]{$S$} circle (2pt);
\obrUhelB[0.75cm]AS[\scriptstyle{60^{\circ}}]B
}}
\def\obrB{
\obrMsr[x=\delka,y=\delka]{-6.5}{6.5}{-5.5}{5.5}
{
\coordinate (A) at (20:2);
\coordinate (B) at (80:2);
\coordinate (S) at (0,0);
\fill[vypln1] (A) -- (B) -- (S) -- cycle;
\draw[thick] (0,0) circle (2);
\draw[thick] (A) -- (S) -- node [sloped,above,xshift=-4pt]{$\scriptstyle{r=4\,\mathrm{cm}}$} (B) -- cycle;
\fill (S) node[below left]{$S$} circle (2pt);
\obrUhelB[0.75cm]AS[\scriptstyle{60^{\circ}}]B
}}
\def\obrC{\obrMsr[x=\delka,y=\delka]{-6.5}{6.5}{-5.5}{5.5}
{
\coordinate (A) at (20:2);
\coordinate (B) at (80:2);
\coordinate (S) at (0,0);
\fill[vypln1] (A) -- (B) arc (80:20:2) -- cycle;
\draw[thick] (0,0) circle (2);
\draw[thick] (A) -- (S) -- node [sloped,above,xshift=-4pt]{$\scriptstyle{r=4\,\mathrm{cm}}$} (B) -- cycle;
\fill (S) node[below left]{$S$} circle (2pt);
\obrUhelB[0.75cm]AS[\scriptstyle{60^{\circ}}]B
}}
\def\obrD{\obrMsr[x=\delka,y=\delka]{-6.5}{6.5}{-5.5}{5.5}
{
\coordinate (A) at (20:2);
\coordinate (B) at (80:2);
\coordinate (S) at (0,0);
\fill[vypln1] (S) circle (2);
\draw[thick] (0,0) circle (2);
\draw[thick] (S) -- node [sloped,above,xshift=-4pt]{$\scriptstyle{r=4\,\mathrm{cm}}$} (B);
\fill (S) node[below left]{$S$} circle (2pt);
}}
\def\obrE{\obrMsr[x=\delka,y=\delka]{-6.5}{6.5}{-5.5}{5.5}
{
\coordinate (A) at (20:2);
\coordinate (B) at (80:2);
\coordinate (C) at (-30:1.5);
\coordinate (S) at (0,0);
\fill[vypln1] (0,0) circle (2);
\draw[thick] (0,0) circle (2);
\draw[thick,fill=white] (0,0) circle (1.5);
\draw[thick] (S) -- node [sloped,above,xshift=-4pt]{$\scriptstyle{r=4\,\mathrm{cm}}$} (B);
\draw[thick] (S) -- node [sloped,above]{$\scriptstyle{3\,\mathrm{cm}}$} (C);
\fill (S) node[below left]{$S$} circle (2pt);
}}
\def\obrF{
\obrMsr[x=\delka,y=\delka]{-6.5}{6.5}{-5.5}{5.5}
{
\coordinate (A) at (20:2);
\coordinate (B) at (80:2);
\coordinate (C) at (-30:1.5);
\coordinate (D) at (20:1.5);
\coordinate (E) at (80:1.5);
\coordinate (S) at (0,0);
\fill[vypln1] (A) arc (20:80:2) -- (E) arc (80:20:1.5) -- cycle;
\draw[thick] (0,0) circle (2);
\draw[thick,fill=white] (0,0) circle (1.5);
\draw[thick] (A) -- (S) -- node [sloped,above,xshift=-4pt]{$\scriptstyle{r=4\,\mathrm{cm}}$} (B);
\draw[thick] (S) -- node [sloped,above]{$\scriptstyle{3\,\mathrm{cm}}$} (C);
\fill (S) node[below left]{$S$} circle (2pt);
\obrUhelB[0.75cm]AS[\scriptstyle{60^{\circ}}]B
}}