1 Oblicz objętość i pole powierzchni prostopadlościanu o podanych wymiarach
a) 8 cm , 9 cm . 10 cm
b) 1/3 m , 3.4 m , 2 1/2 m
c ) pierwiastek z dwóch , pierwiastek z ośmiu , i pierwiastek z 32
2 oblicz objętośc i pole powierzchni sześcianu o podanej długości kraedzi
a) 9 cm
b) 2,5 cm
c) 3 1/3 m
d pierwiastek z 5
krysta
![Zad.1\\a)\\ a=8 [cm] \\ b=9 [cm] \\h=10 [cm] \\V = P_{p}\cdot h\\P_{p}=a\cdot b\\P_{p}=8\cdot 9=72[cm^{2}]\\V=72\cdot 10=720 [cm^{3}]\\P_{c}=2P_{p}+P_{b}\\P_{b}=(2a+2b)\cdot h](https://tex.z-dn.net/?f=Zad.1%5C%5Ca%29%5C%5C+a%3D8+%5Bcm%5D+%5C%5C+b%3D9+%5Bcm%5D+%5C%5Ch%3D10+%5Bcm%5D+%5C%5CV+%3D+P_%7Bp%7D%5Ccdot+h%5C%5CP_%7Bp%7D%3Da%5Ccdot+b%5C%5CP_%7Bp%7D%3D8%5Ccdot+9%3D72%5Bcm%5E%7B2%7D%5D%5C%5CV%3D72%5Ccdot+10%3D720+%5Bcm%5E%7B3%7D%5D%5C%5CP_%7Bc%7D%3D2P_%7Bp%7D%2BP_%7Bb%7D%5C%5CP_%7Bb%7D%3D%282a%2B2b%29%5Ccdot+h "Zad.1\\a)\\ a=8 [cm] \\ b=9 [cm] \\h=10 [cm] \\V = P_{p}\cdot h\\P_{p}=a\cdot b\\P_{p}=8\cdot 9=72[cm^{2}]\\V=72\cdot 10=720 [cm^{3}]\\P_{c}=2P_{p}+P_{b}\\P_{b}=(2a+2b)\cdot h")
![Pb=(2\cdot 8+2\cdot 9)\cdot 10=(16+18)\cdot 10=34\cdot 10=340[cm^{2}]\\Pc=2\cdot 78+340=156+340=496 [cm^{2}]](https://tex.z-dn.net/?f=Pb%3D%282%5Ccdot+8%2B2%5Ccdot+9%29%5Ccdot+10%3D%2816%2B18%29%5Ccdot+10%3D34%5Ccdot+10%3D340%5Bcm%5E%7B2%7D%5D%5C%5CPc%3D2%5Ccdot+78%2B340%3D156%2B340%3D496+%5Bcm%5E%7B2%7D%5D "Pb=(2\cdot 8+2\cdot 9)\cdot 10=(16+18)\cdot 10=34\cdot 10=340[cm^{2}]\\Pc=2\cdot 78+340=156+340=496 [cm^{2}]")
![b)\\a=\frac{1}{3} [m] \\ b=3,4 [m] \\h=2\frac{1}{2} [m]\\V = P_{p}\cdot h\\P_{p}=a\cdot b\\P_{p}=\frac{1}{3}\cdot3,4=\frac{1}{3}\cdot\frac{34}{10}=\frac{17}{15}=1\frac{2}{15}[m^{2}]\\V=1\frac{2}{15}\cdot 2\frac{1}{2}=\frac{17}{15}\cdot \frac{5}{2} =\frac{17}{6}=2\frac{5}{6}[cm^{3}]](https://tex.z-dn.net/?f=b%29%5C%5Ca%3D%5Cfrac%7B1%7D%7B3%7D+%5Bm%5D+%5C%5C+b%3D3%2C4+%5Bm%5D+%5C%5Ch%3D2%5Cfrac%7B1%7D%7B2%7D+%5Bm%5D%5C%5CV+%3D+P_%7Bp%7D%5Ccdot+h%5C%5CP_%7Bp%7D%3Da%5Ccdot+b%5C%5CP_%7Bp%7D%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot3%2C4%3D%5Cfrac%7B1%7D%7B3%7D%5Ccdot%5Cfrac%7B34%7D%7B10%7D%3D%5Cfrac%7B17%7D%7B15%7D%3D1%5Cfrac%7B2%7D%7B15%7D%5Bm%5E%7B2%7D%5D%5C%5CV%3D1%5Cfrac%7B2%7D%7B15%7D%5Ccdot+2%5Cfrac%7B1%7D%7B2%7D%3D%5Cfrac%7B17%7D%7B15%7D%5Ccdot+%5Cfrac%7B5%7D%7B2%7D+%3D%5Cfrac%7B17%7D%7B6%7D%3D2%5Cfrac%7B5%7D%7B6%7D%5Bcm%5E%7B3%7D%5D "b)\\a=\frac{1}{3} [m] \\ b=3,4 [m] \\h=2\frac{1}{2} [m]\\V = P_{p}\cdot h\\P_{p}=a\cdot b\\P_{p}=\frac{1}{3}\cdot3,4=\frac{1}{3}\cdot\frac{34}{10}=\frac{17}{15}=1\frac{2}{15}[m^{2}]\\V=1\frac{2}{15}\cdot 2\frac{1}{2}=\frac{17}{15}\cdot \frac{5}{2} =\frac{17}{6}=2\frac{5}{6}[cm^{3}]")
![P_{c}=2P_{p}+P_{b}\\P_{b}=(2a+2b)\cdot h\\Pb=(2\cdot \frac{1}{3}+2\cdot 3,4)\cdot \frac{5}{2}=(\frac{2}{3}+6,8)\cdot \frac{5}{2}=(\frac{2}{3}+\frac{68}{10})\cdot \frac{5}{2}=\\(\frac{2}{3}+6,8)\cdot \frac{5}{2}=(\frac{2}{3}+\frac{34}{5})\cdot \frac{5}{2}=(\frac{10}{15}+\frac{102}{15})\cdot \frac{5}{2}=\\\frac{112}{15}\cdot \frac{5}{2}=\frac{56}{3}= 18\frac{2}{3}[cm^2]](https://tex.z-dn.net/?f=P_%7Bc%7D%3D2P_%7Bp%7D%2BP_%7Bb%7D%5C%5CP_%7Bb%7D%3D%282a%2B2b%29%5Ccdot+h%5C%5CPb%3D%282%5Ccdot+%5Cfrac%7B1%7D%7B3%7D%2B2%5Ccdot+3%2C4%29%5Ccdot+%5Cfrac%7B5%7D%7B2%7D%3D%28%5Cfrac%7B2%7D%7B3%7D%2B6%2C8%29%5Ccdot+%5Cfrac%7B5%7D%7B2%7D%3D%28%5Cfrac%7B2%7D%7B3%7D%2B%5Cfrac%7B68%7D%7B10%7D%29%5Ccdot+%5Cfrac%7B5%7D%7B2%7D%3D%5C%5C%28%5Cfrac%7B2%7D%7B3%7D%2B6%2C8%29%5Ccdot+%5Cfrac%7B5%7D%7B2%7D%3D%28%5Cfrac%7B2%7D%7B3%7D%2B%5Cfrac%7B34%7D%7B5%7D%29%5Ccdot+%5Cfrac%7B5%7D%7B2%7D%3D%28%5Cfrac%7B10%7D%7B15%7D%2B%5Cfrac%7B102%7D%7B15%7D%29%5Ccdot+%5Cfrac%7B5%7D%7B2%7D%3D%5C%5C%5Cfrac%7B112%7D%7B15%7D%5Ccdot+%5Cfrac%7B5%7D%7B2%7D%3D%5Cfrac%7B56%7D%7B3%7D%3D+18%5Cfrac%7B2%7D%7B3%7D%5Bcm%5E2%5D "P_{c}=2P_{p}+P_{b}\\P_{b}=(2a+2b)\cdot h\\Pb=(2\cdot \frac{1}{3}+2\cdot 3,4)\cdot \frac{5}{2}=(\frac{2}{3}+6,8)\cdot \frac{5}{2}=(\frac{2}{3}+\frac{68}{10})\cdot \frac{5}{2}=\\(\frac{2}{3}+6,8)\cdot \frac{5}{2}=(\frac{2}{3}+\frac{34}{5})\cdot \frac{5}{2}=(\frac{10}{15}+\frac{102}{15})\cdot \frac{5}{2}=\\\frac{112}{15}\cdot \frac{5}{2}=\frac{56}{3}= 18\frac{2}{3}[cm^2]")
![zad.2\\a) \\a=9 [cm] \\V=a^{3} \\V=9^{3}=729 [cm^{3}]\\P_{c}=6a^{2}\\P_{c}=6\cdot 9^{2}=6\cdot 81=486 [cm^{2}]](https://tex.z-dn.net/?f=zad.2%5C%5Ca%29+%5C%5Ca%3D9+%5Bcm%5D+%5C%5CV%3Da%5E%7B3%7D+%5C%5CV%3D9%5E%7B3%7D%3D729+%5Bcm%5E%7B3%7D%5D%5C%5CP_%7Bc%7D%3D6a%5E%7B2%7D%5C%5CP_%7Bc%7D%3D6%5Ccdot+9%5E%7B2%7D%3D6%5Ccdot+81%3D486+%5Bcm%5E%7B2%7D%5D "zad.2\\a) \\a=9 [cm] \\V=a^{3} \\V=9^{3}=729 [cm^{3}]\\P_{c}=6a^{2}\\P_{c}=6\cdot 9^{2}=6\cdot 81=486 [cm^{2}]")
![b) \\a=[2,5 [cm] \\V=a^{3} \\V=(2,5)^{3}=15,625 [cm^{3}]\\P_{c}=6a^{2}\\P_{c}=6\cdot (2,5)^{2}=6\cdot6,25=37,5 [cm^{2}]](https://tex.z-dn.net/?f=b%29+%5C%5Ca%3D%5B2%2C5+%5Bcm%5D+%5C%5CV%3Da%5E%7B3%7D+%5C%5CV%3D%282%2C5%29%5E%7B3%7D%3D15%2C625+%5Bcm%5E%7B3%7D%5D%5C%5CP_%7Bc%7D%3D6a%5E%7B2%7D%5C%5CP_%7Bc%7D%3D6%5Ccdot+%282%2C5%29%5E%7B2%7D%3D6%5Ccdot6%2C25%3D37%2C5+%5Bcm%5E%7B2%7D%5D "b) \\a=[2,5 [cm] \\V=a^{3} \\V=(2,5)^{3}=15,625 [cm^{3}]\\P_{c}=6a^{2}\\P_{c}=6\cdot (2,5)^{2}=6\cdot6,25=37,5 [cm^{2}]")
![c) \\a=3\frac{1}{3} [m] \\V=a^{3}\\V=(3\frac{1}{3})^{3}=(\frac{10}{3})^{3}=\frac{1000}{27}=37\frac{1}{27}[cm^{3}]\\P_{c}=6a^{2}\\P_{c}=6\cdot (3\frac{1}{3})^{2}=6\cdot(\frac{100}{3})^{2}=6\cdot \frac{100}{9}=\frac{200}{3}=66\frac{2}{3}[m^{3}]](https://tex.z-dn.net/?f=c%29+%5C%5Ca%3D3%5Cfrac%7B1%7D%7B3%7D+%5Bm%5D+%5C%5CV%3Da%5E%7B3%7D%5C%5CV%3D%283%5Cfrac%7B1%7D%7B3%7D%29%5E%7B3%7D%3D%28%5Cfrac%7B10%7D%7B3%7D%29%5E%7B3%7D%3D%5Cfrac%7B1000%7D%7B27%7D%3D37%5Cfrac%7B1%7D%7B27%7D%5Bcm%5E%7B3%7D%5D%5C%5CP_%7Bc%7D%3D6a%5E%7B2%7D%5C%5CP_%7Bc%7D%3D6%5Ccdot+%283%5Cfrac%7B1%7D%7B3%7D%29%5E%7B2%7D%3D6%5Ccdot%28%5Cfrac%7B100%7D%7B3%7D%29%5E%7B2%7D%3D6%5Ccdot+%5Cfrac%7B100%7D%7B9%7D%3D%5Cfrac%7B200%7D%7B3%7D%3D66%5Cfrac%7B2%7D%7B3%7D%5Bm%5E%7B3%7D%5D "c) \\a=3\frac{1}{3} [m] \\V=a^{3}\\V=(3\frac{1}{3})^{3}=(\frac{10}{3})^{3}=\frac{1000}{27}=37\frac{1}{27}[cm^{3}]\\P_{c}=6a^{2}\\P_{c}=6\cdot (3\frac{1}{3})^{2}=6\cdot(\frac{100}{3})^{2}=6\cdot \frac{100}{9}=\frac{200}{3}=66\frac{2}{3}[m^{3}]")
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