walec
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H- wysokość walca
r- promień podstawy walca
\(\frac{H}{8\sqrt{2}}=cos60^0\\\frac{H}{8\sqrt{2}}=\frac{1}{2}\\H=4\sqrt{2}\)
Drugi bok tego prostokąta to obwód podstawy walca:
\(\frac{2\pi\ r}{8\sqrt{2}}=sin60^0\\\frac{2\pi\ r}{8\sqrt{2}}=\frac{\sqrt{3}}{2}\\4\pi\ r=8\sqrt{6}\\r=\frac{2\sqrt{6}}{\pi}\)
Objętość walca:
\(V=\pi\ r^2H\\v=\pi\cdot(\frac{2\sqrt{6}}{\pi})^2\cdot4\sqrt{2}=\pi\cdot\frac{24}{\p^2}\cdot4\sqrt{2}=\frac{96\sqrt{2}}{\pi}\)
r- promień podstawy walca
\(\frac{H}{8\sqrt{2}}=cos60^0\\\frac{H}{8\sqrt{2}}=\frac{1}{2}\\H=4\sqrt{2}\)
Drugi bok tego prostokąta to obwód podstawy walca:
\(\frac{2\pi\ r}{8\sqrt{2}}=sin60^0\\\frac{2\pi\ r}{8\sqrt{2}}=\frac{\sqrt{3}}{2}\\4\pi\ r=8\sqrt{6}\\r=\frac{2\sqrt{6}}{\pi}\)
Objętość walca:
\(V=\pi\ r^2H\\v=\pi\cdot(\frac{2\sqrt{6}}{\pi})^2\cdot4\sqrt{2}=\pi\cdot\frac{24}{\p^2}\cdot4\sqrt{2}=\frac{96\sqrt{2}}{\pi}\)
\(d=8\sqrt{2}\)
\(cos60^o = \frac{h}{d}\)
\(\frac{1}{2} = \frac{h}{8\sqrt{2}}\)
\(h=4\sqrt{2}\)
\(2\pi r=\sqrt{d^2-h^2} = \sqrt{128-32} = \sqrt{96} = 4\sqrt{6}\)
\(2\pi r = 4\sqrt{6} \Rightarrow r=\frac{2\sqrt{6}}{\pi}\)
\(V=\pi r^2 \cdot h = \pi \cdot \(\frac{2\sqrt{6}}{\pi}\)^2 \cdot 4\sqrt{2} = \frac{96\sqrt{2}}{\pi} \ j^3\)
\(cos60^o = \frac{h}{d}\)
\(\frac{1}{2} = \frac{h}{8\sqrt{2}}\)
\(h=4\sqrt{2}\)
\(2\pi r=\sqrt{d^2-h^2} = \sqrt{128-32} = \sqrt{96} = 4\sqrt{6}\)
\(2\pi r = 4\sqrt{6} \Rightarrow r=\frac{2\sqrt{6}}{\pi}\)
\(V=\pi r^2 \cdot h = \pi \cdot \(\frac{2\sqrt{6}}{\pi}\)^2 \cdot 4\sqrt{2} = \frac{96\sqrt{2}}{\pi} \ j^3\)