$V_{\text{Zylinder}}=r^2\cdot \pi \cdot hV\_\{\backslash text\{Zylinder\}\}=r^2\backslash cdot\backslash pi\backslash cdot\; h$

$r={\displaystyle \frac{d}{2}}r=\backslash displaystyle\backslash dfrac\{d\}\{2\}$

$r=\frac{7}{2}=\mathrm{3,5}r=\backslash frac\{7\}\{2\}=3\{,\}5$

$h=3\text{ cm}h=3\backslash cm$

$V={\mathrm{3,5}}^2\cdot \pi \cdot 3\approx \mathrm{115,453}V=3\{,\}5^2\backslash cdot\backslash pi\backslash cdot3\backslash approx115\{,\}453$

$V_{\text{Halbzylinder}}=\mathrm{115,453}:2\approx \mathrm{57,73}V\_\{\backslash text\{Halbzylinder\}\}=115\{,\}453:2\backslash approx57\{,\}73$

Der obere Halbzylinder hat ein Volumen von $\mathrm{57,73}{\text{ cm}}^{3}57\{,\}73\backslash cm^3$.

$V_{Zylinder}=r^2\cdot \pi \cdot hV\_\{Zylinder\}=r^2\backslash cdot\backslash pi\backslash cdot\; h$

$V=190{\text{ cm}}^{3}V=190\backslash cm^3$

$r=\mathrm{3,5}\text{ cm}r=3\{,\}5\backslash cm$

$190={\mathrm{3,5}}^2\cdot \pi \cdot h190=3\{,\}5^2\backslash cdot\backslash pi\backslash cdot\; h$

$h={\displaystyle \frac{190}{\mathrm{12,25}\cdot \pi }}h=\backslash displaystyle\backslash frac\{190\}\{12\{,\}25\backslash cdot\backslash pi\}$

$h\approx \mathrm{4,94}h\backslash approx4\{,\}94$

Der untere Zylinder hat eine Höhe von $\approx \mathrm{4,94}\text{ cm}\mathrm{.}\backslash approx\; 4\{,\}94\backslash cm.$

$V_{\text{Werkst}\ddot{\text{u}}\text{ck}}=\mathrm{57,73}+190=\mathrm{247,73}V\_\{\backslash text\{Werkstück\}\}=57\{,\}73+190=247\{,\}73$

Masse: m

$m_{\text{Werkst}\ddot{\text{u}}\text{ck}}=\mathrm{247,73}\cdot \mathrm{7,86}=\mathrm{1947,16}m\_\{\backslash text\{Werkstück\}\}=247\{,\}73\backslash cdot7\{,\}86=1947\{,\}16$

${}_{}\_\{\; \}$

Das Werkstück hat eine Masse von $\mathrm{1947,16}g1947\{,\}16\backslash \; g$.