1. Olicz pole powierzchni i objętość kuli o podanym ptomieniu
a) 4 1/2 cm
2. Olicz promień kuli o podanej objętości
a) 4 \frac {1}{2} \pi cm^{3}
b) 166 \frac {2}{3} \pi cm^{3}
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Zad.1
Zad.2
a)
b)![V=166 \frac {2}{3} \pi cm^{3}=\frac{500}{3}\pi cm^3\\\frac{4}{3}\pi R^3=\frac{500}{3}\pi/:\frac{4}{3}\pi\\\R^3=\frac{500}{3}\cdot\frac{3}{4}\\R^3=\frac{500}{4}\\\\R=\sqrt[3]{\frac{500}{4}}\\\\R=\frac{5\sqrt[3]{4}}{\sqrt[3]{4}=5cm V=166 \frac {2}{3} \pi cm^{3}=\frac{500}{3}\pi cm^3\\\frac{4}{3}\pi R^3=\frac{500}{3}\pi/:\frac{4}{3}\pi\\\R^3=\frac{500}{3}\cdot\frac{3}{4}\\R^3=\frac{500}{4}\\\\R=\sqrt[3]{\frac{500}{4}}\\\\R=\frac{5\sqrt[3]{4}}{\sqrt[3]{4}=5cm](https://tex.z-dn.net/?f=V%3D166+%5Cfrac+%7B2%7D%7B3%7D+%5Cpi+cm%5E%7B3%7D%3D%5Cfrac%7B500%7D%7B3%7D%5Cpi+cm%5E3%5C%5C%5Cfrac%7B4%7D%7B3%7D%5Cpi+R%5E3%3D%5Cfrac%7B500%7D%7B3%7D%5Cpi%2F%3A%5Cfrac%7B4%7D%7B3%7D%5Cpi%5C%5C%5CR%5E3%3D%5Cfrac%7B500%7D%7B3%7D%5Ccdot%5Cfrac%7B3%7D%7B4%7D%5C%5CR%5E3%3D%5Cfrac%7B500%7D%7B4%7D%5C%5C%5C%5CR%3D%5Csqrt%5B3%5D%7B%5Cfrac%7B500%7D%7B4%7D%7D%5C%5C%5C%5CR%3D%5Cfrac%7B5%5Csqrt%5B3%5D%7B4%7D%7D%7B%5Csqrt%5B3%5D%7B4%7D%3D5cm)