Objętość bryły

Project ID: 
6000000009
Accepted: 
Podobszar: 
Typ: 
Layout: 
Question: 
Dopasuj każdą bryłę do wzoru, którego można użyć do obliczenia jej objętości.
Tex: 
% http://math4u.vsb.cz/ticket/32562 \definecolor{Maroon}{rgb}{0.76, 0.13, 0.28} \usetikzlibrary{arrows,calc} \makeatletter% % \pgfkeys{ % /tkzcone/.cd, % } \define@cmdkey[TKZ]{ell}{color}{} \define@cmdkey[TKZ]{ell}{shift}{} \presetkeys[TKZ]{ell}{color = {},shift = 0}{} % (#2,#3) coordonnĂŠe du centre (#4,#5) Ra et Rb \newcommand*{\ellipseThreeD}[1][]{\tkz@ellipseThreeD[#1]}% \def\tkz@ellipseThreeD[#1](#2,#3)(#4,#5){% \setkeys[TKZ]{ell}{#1}% \draw[yshift=\cmdTKZ@ell@shift cm,dashed] (#4,0) arc(0:180:#4 and #5); \draw[yshift=\cmdTKZ@ell@shift cm ] (-#4,0) arc(180:360:#4 and #5); \path[fill=\cmdTKZ@ell@color,opacity=0.5,shade](#2 cm,#3 cm) ellipse (#4 and #5); } \newcommand*{\sellipseThreeD}[1][]{\tkz@sellipseThreeD[#1]}% \def\tkz@sellipseThreeD[#1](#2,#3)(#4,#5){% \setkeys[TKZ]{ell}{#1}% \draw[yshift=\cmdTKZ@ell@shift cm,dashed] (#4,0) arc(0:180:#4 and #5); \draw[yshift=\cmdTKZ@ell@shift cm ] (-#4,0) arc(180:360:#4 and #5); } \def\tkzCone{\pgfutil@ifnextchar[{\tkz@cone}{\tkz@cone[]}} \def\tkz@cone[#1]#2#3#4{% % #1 styles % #2 rayon R % #3 coeff d'aplatissement k % #4 Hauteur du cĂ´ne H % \pgfkeys{% % /tkzcone/.cd % }% % \pgfqkeys{/tkzcone}{#1}% \pgfmathsetmacro{\bb}{#2*#3} \pgfmathsetmacro{\yy}{\bb*\bb/#4} \pgfmathsetmacro{\xx}{#2*sqrt((1-\yy)/#4)} \fill[color=Maroon!10] (0,#4)--(-\xx,\yy) arc(180:360:\xx cm and .5 cm); \ellipseThreeD[color=Maroon!30](0,0)(\xx cm,.5 cm) \draw (0,#4)--(\xx,\yy); \draw (0,#4)--(-\xx,\yy); \draw[dashed] (0,0) -- node[right] {$5$} (0,#4); \draw[dashed] (0,0) -- node[below] {$3$} (1.75cm,0); }% \def\tkzCylinder{\pgfutil@ifnextchar[{\tkz@cylinder}{\tkz@cylinder[]}} \def\tkz@cylinder[#1]#2#3#4{% \pgfmathsetmacro{\bb}{#2*#3} \pgfmathsetmacro{\yy}{\bb*\bb/#4} \pgfmathsetmacro{\xx}{#2*sqrt((1-\yy)/#4)} \fill[color=Maroon!10] (-\xx cm,0)--(-\xx cm,#4 cm) arc(180:360:\xx cm and .5 cm)--(\xx cm,0) arc(360:180:\xx cm and .5 cm); \ellipseThreeD[color=Maroon!30](0,0)(\xx cm,.5 cm) \begin{scope}[yshift=#4 cm] \draw[fill=\cmdTKZ@ell@color,opacity=0.5,shade](0,0) ellipse (\xx cm and .5 cm) ; \end{scope} \draw (\xx cm,0)--(\xx cm,#4 cm); \draw (-\xx cm,0)--(-\xx cm,#4 cm); \draw (-1pt,-1pt)--(1pt,1pt); \draw (1pt,-1pt)--(-1pt,1pt); \begin{scope}[yshift=5cm] \draw (-1pt,-1pt)--(1pt,1pt); \draw (1pt,-1pt)--(-1pt,1pt); \draw[dashed] (0,0)--node[below]{$5$}(1.8 cm,0); \end{scope} \draw (2cm,2.5cm) node[right] {$7$}; }% \def\tkzTruncatedCone{\pgfutil@ifnextchar[{\tkz@TruncatedCone}{\tkz@TruncatedCone[]}} \def\tkz@TruncatedCone[#1]#2#3#4{% \pgfmathsetmacro{\bb}{#2*#3} \pgfmathsetmacro{\yy}{\bb*\bb/#4} \pgfmathsetmacro{\xx}{#2*sqrt((1-\yy)/#4)} \fill[color=Maroon!10] (-\xx cm,0)--(-0.5*\xx cm,#4 cm) arc(180:360:0.5*\xx cm and .25 cm)--(\xx cm,0) arc(360:180:\xx cm and .5 cm); \ellipseThreeD[color=Maroon!30](0,0)(\xx cm,.5 cm) \begin{scope}[yshift=#4 cm] \draw[fill=\cmdTKZ@ell@color,opacity=0.5,shade](0,0) ellipse (0.5*\xx cm and .25 cm); \end{scope} \draw (\xx cm,0)--(0.5*\xx cm,#4 cm); \draw (-\xx cm,0)--(-0.5*\xx cm,#4 cm); \draw[dashed] (0,0) -- node[right] {$5$} (0,#4); \draw[dashed] (0,0) -- node[below] {$3$} (2.2cm,0); \draw[dashed] (0,#4) -- node[above] {$1$} (1cm,#4); }% \def\tkzSphere{\pgfutil@ifnextchar[{\tkz@Sphere}{\tkz@Sphere[]}} \def\tkz@Sphere[#1]#2#3#4{% \pgfmathsetmacro{\bb}{#2*#3} \pgfmathsetmacro{\yy}{\bb*\bb/#4} \pgfmathsetmacro{\xx}{#2*sqrt((1-\yy)/#4)} \filldraw[ball color=Maroon!10] (0,0) circle[radius=\xx]; \sellipseThreeD(0,0)(\xx cm,.65 cm) \begin{scope}[rotate=-90] %\sellipseThreeD(0,0)(\xx cm,.25 cm) \draw[dashed] (0,0)-- node[below]{$2$} (0,\xx cm); \draw (-1pt,-1pt)--(1pt,1pt); \draw (1pt,-1pt)--(-1pt,1pt); \end{scope} }% \newcommand{\parapp}[3]{% \fill[Maroon!10,opacity=.5] (0,0,0)-- (#1,0,0) -- (#1,#3,0) -- (0,#3,0) --cycle; \fill[Maroon!10,opacity=.5] (0,0,#2)-- (#1,0,#2) -- (#1,#3,#2) -- (0,#3,#2) --cycle; \fill[Maroon!10,opacity=.5] (0,#3,0)-- (0,#3,#2) -- (#1,#3,#2) -- (#1,#3,0)--cycle; \fill[Maroon!10,opacity=.5] (0,0,0)-- (0,0,#2) -- (#1,0,#2) -- (#1,0,0)--cycle; \draw[] (0,0,#2) -- (#1,0,#2) -- (#1,#3,#2) --(0,#3,#2) --(0,0,#2) (#1,0,#2) -- (#1,0,0) -- (#1,#3,0) --(0,#3,0) -- (0,#3,#2) (#1,#3,#2) -- (#1,#3,0); \draw[dashed] (0,0,0) -- (0,0,#2) (0,0,0)-- (#1,0,0) (0,0,0)-- (0,#3,0); } \otazka{ \begin{tikzpicture}[scale=0.6] \tkzCylinder{4}{0}{5}\end{tikzpicture}}{$\pi\int_2^9 25\,\mathrm{d}x$} \otazka{ \begin{tikzpicture}[scale=0.6] \tkzCone{4}{0}{5}\end{tikzpicture}}{$\pi\int_0^5 \frac{9}{25}x^2\,\mathrm{d}x$} \otazka{ \begin{tikzpicture}[scale=0.6] \tkzTruncatedCone{5}{0}{5}\end{tikzpicture}}{$\pi\int_0^5 \left( \frac 25 x+1\right)^2\,\mathrm{d}x$} \otazka{ \begin{tikzpicture}[scale=0.6] \tkzSphere{4}{0}{4}\end{tikzpicture}}{$\pi\int_0^4 [4-(x-2)^2]\,\mathrm{d}x$} \fake{$\pi\int_2^9 5\,\mathrm{d}x$} \fake{$\pi\int_0^5 \frac 35 x^2\,\mathrm{d}x$} \NastavOT{4}