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Version 12.1 von Bastian Knöpfle am 2026/02/03 10:59
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1 Würfel:
2 {{formula}}V=a^3=1000 \mathrm{cm}^3 \Rightarrow a=10\mathrm{cm}{{/formula}}
3
4 {{formula}}O=6 \cdot a^2=600\mathrm{cm}^2{{/formula}}
5
6 Kugel:
7 {{formula}}V=\frac{4}{3} \cdot \pi r^3 =1000 \mathrm{cm}^3 \Rightarrow r=\sqrt[3]{\frac{3V}{4 \pi}} =\sqrt[3]{\frac{3 \cdot 1000}{4 \pi}} =6,2 \mathrm{cm} {{/formula}}
8
9 {{formula}}O=4 \pi \cdot r^2 = 4 \pi (6,2 \mathrm{cm})^2 =483 \mathrm{cm}^2 {{/formula}}
10
11 Zyliner:
12 {{formula}}V=\pi \cdot r^2 \cdot h \quad \text{mit} \quad h=2r {{/formula}}
13 {{formula}} V=2 \pi r^3{{/formula}}
14 {{formula}} r=\sqrt[3]{\frac{V}{2 \pi}}=\sqrt[3]{\frac{1000}{2 \pi}}=5,42\mathrm{cm}{{/formula}}
15
16 {{formula}} O=2 \pi \cdot r^2+2\pi \cdot r \cdot h \quad \text{mit} \quad h=2r {{/formula}}
17 {{formula}} O=2 \pi \cdot r^2+2\pi \cdot r \cdot 2r {{/formula}}
18 {{formula}} O=2 \pi \cdot r^2+4\pi \cdot r^2 {{/formula}}
19 {{formula}} O=2 \pi \cdot (5,42\mathrm{cm})^2+4\pi \cdot (5,42\mathrm{cm})^2=553,6 \mathrm{cm}^2 {{/formula}}