I.
[tex]a = 3,5 \ cm\\\\P_{c} = 6a^{2} = 6\cdot(3,5 \ cm)^{2} = 6\cdot12,75 \ cm^{2}=73,5 \ cm^{2}\\\\V = a^{3} = (3,5 \ cm)^{3} = 42,875 \ cm^{3}[/tex]
II.
[tex]P_{p} = 49 \ cm^{2}\\H = 11 \ cm\\V = ?\\P_{b} = ?\\\\V = P_{p}\cdot H = 49 \ cm^{2}\cdot11 \ cm = 539 \ cm^{3}\\\\\\P_{p} = a^{2} = 49 \ cm^{2}\\\\a^{2} = 49 \ cm^{2}\\\\a = \sqrt{49 \ cm^{2}}\\\\a = 7 \ cm\\\\P_{b} = 4aH = 4\cdot7 \ cm \cdot 11 \ cm = 308 \ cm^{2}[/tex]
III.
[tex]a = 5 \ cm\\b = 6 \ cm\\V = 360 \ cm^{3}\\H = ?\\P_{c} = ?\\\\P_{p} = a\cdot b = 5 \ cm\cdot6 \ cm = 30 \ cm^{2}\\\\V = P_{p}\cdot H \ \ /:P_{p}\\\\H = \frac{V}{P_{p}} = \frac{360 \ cm^{3}}{30 \ cm^{2}} = 12 \ cm\\\\\\P_{c} = 2P_{p} +P_{b}\\\\P_{b} = 2aH + 2bH = 2H(a+b) = 2\cdot12 \ cm\cdot(5 \ cm + 6 \ cm) = 24 \ cm\cdot11 \ cm = 264 \ cm^{2}\\\\P_{c} = 2\cdot30 \ cm^{2}+264 \ cm^{2} = 60 \ cm^{2}+264 \ cm^{2} = 324 \ cm^{2}[/tex]
IV.
a - długość krawędzi sześcianu
12a - długość wszystkich krawędzi
Pc = ?
V = ?
[tex]12a = 3,6 \ dm \ \ /:12\\\\a = 0,3 \ dm\\\\P_{c} = 6a^{2} = 6\cdot(0,3 \ dm)^{2} = 6\cdot0,09 \ dm^{2} = 0,54 \ dm^{2}\\\\V = a^{3} = (0,3 \ dm)^{3} = 0,027 \ dm^{3}[/tex]
V.
[tex]V = 125 \ cm^{3}\\i\\V = a^{3}\\\\a^{3} = 125 \ cm^{3}\\\\a = \sqrt[3]{125 \ cm^{3}}\\\\a = 5 \ cm[/tex]
Rysujesz 6 kwadratów o boku a = 5 cm (bo sześcian ma 6 ścian).
Np: 4 kwadraty w poziomie i za pierwszym kwadratem od lewej dodatkowo 2 w pionie.
