1.Przekątna sześcianu ma długość 12cm. Oblicz objętość tego sześcianu
2.Przekątna sześcianu ma długość 10cm. Oblicz objętość tego sześcianu
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1.![d---przekatna\ szescianu\\d=a\sqrt{3}\\12=a\sqrt{3}\ \ \ /:\sqrt{3}\\\frac{12}{\sqrt{3}}=a\\\frac{12}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}=a\\\frac{12\sqrt{3}}{3}=a\\V=a^3\\V=(\frac{12\sqrt{3}}{3})^3\\V=\frac{12^3*(\sqrt{3})^3}{3^3}\\V=\frac{1728*3\sqrt{3}}{27}\\V=64*3\sqrt{3}=192\sqrt{3}cm^3 d---przekatna\ szescianu\\d=a\sqrt{3}\\12=a\sqrt{3}\ \ \ /:\sqrt{3}\\\frac{12}{\sqrt{3}}=a\\\frac{12}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}=a\\\frac{12\sqrt{3}}{3}=a\\V=a^3\\V=(\frac{12\sqrt{3}}{3})^3\\V=\frac{12^3*(\sqrt{3})^3}{3^3}\\V=\frac{1728*3\sqrt{3}}{27}\\V=64*3\sqrt{3}=192\sqrt{3}cm^3](https://tex.z-dn.net/?f=+d---przekatna%5C+szescianu%5C%5Cd%3Da%5Csqrt%7B3%7D%5C%5C12%3Da%5Csqrt%7B3%7D%5C+%5C+%5C+%2F%3A%5Csqrt%7B3%7D%5C%5C%5Cfrac%7B12%7D%7B%5Csqrt%7B3%7D%7D%3Da%5C%5C%5Cfrac%7B12%7D%7B%5Csqrt%7B3%7D%7D%2A%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B3%7D%7D%3Da%5C%5C%5Cfrac%7B12%5Csqrt%7B3%7D%7D%7B3%7D%3Da%5C%5CV%3Da%5E3%5C%5CV%3D%28%5Cfrac%7B12%5Csqrt%7B3%7D%7D%7B3%7D%29%5E3%5C%5CV%3D%5Cfrac%7B12%5E3%2A%28%5Csqrt%7B3%7D%29%5E3%7D%7B3%5E3%7D%5C%5CV%3D%5Cfrac%7B1728%2A3%5Csqrt%7B3%7D%7D%7B27%7D%5C%5CV%3D64%2A3%5Csqrt%7B3%7D%3D192%5Csqrt%7B3%7Dcm%5E3)
2.![d---przekatna\ szescianu\\d=a\sqrt{3}\\10=a\sqrt{3}\ \ \ /:\sqrt{3}\\\frac{10}{\sqrt{3}}=a\\\frac{10}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}=a\\\frac{10\sqrt{3}}{3}=a\\V=a^3\\V=(\frac{10\sqrt{3}}{3})^3\\V=\frac{10^3*(\sqrt{3})^3}{3^3}\\V=\frac{1000*3\sqrt{3}}{27}\\V=\frac{3000\sqrt{3}}{27}\\V=\frac{1000\sqrt{3}}{9}cm^3 d---przekatna\ szescianu\\d=a\sqrt{3}\\10=a\sqrt{3}\ \ \ /:\sqrt{3}\\\frac{10}{\sqrt{3}}=a\\\frac{10}{\sqrt{3}}*\frac{\sqrt{3}}{\sqrt{3}}=a\\\frac{10\sqrt{3}}{3}=a\\V=a^3\\V=(\frac{10\sqrt{3}}{3})^3\\V=\frac{10^3*(\sqrt{3})^3}{3^3}\\V=\frac{1000*3\sqrt{3}}{27}\\V=\frac{3000\sqrt{3}}{27}\\V=\frac{1000\sqrt{3}}{9}cm^3](https://tex.z-dn.net/?f=d---przekatna%5C+szescianu%5C%5Cd%3Da%5Csqrt%7B3%7D%5C%5C10%3Da%5Csqrt%7B3%7D%5C+%5C+%5C+%2F%3A%5Csqrt%7B3%7D%5C%5C%5Cfrac%7B10%7D%7B%5Csqrt%7B3%7D%7D%3Da%5C%5C%5Cfrac%7B10%7D%7B%5Csqrt%7B3%7D%7D%2A%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Csqrt%7B3%7D%7D%3Da%5C%5C%5Cfrac%7B10%5Csqrt%7B3%7D%7D%7B3%7D%3Da%5C%5CV%3Da%5E3%5C%5CV%3D%28%5Cfrac%7B10%5Csqrt%7B3%7D%7D%7B3%7D%29%5E3%5C%5CV%3D%5Cfrac%7B10%5E3%2A%28%5Csqrt%7B3%7D%29%5E3%7D%7B3%5E3%7D%5C%5CV%3D%5Cfrac%7B1000%2A3%5Csqrt%7B3%7D%7D%7B27%7D%5C%5CV%3D%5Cfrac%7B3000%5Csqrt%7B3%7D%7D%7B27%7D%5C%5CV%3D%5Cfrac%7B1000%5Csqrt%7B3%7D%7D%7B9%7Dcm%5E3)