Largest possible sphere is cut from a cubr of side 7 cm
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Side = 7cm
![volume = {(7)}^{3} = 343 {cm}^{3} \\ \\ sphere) \\ \\ v = \frac{4}{3}\pi {r}^{3} \\ 343 = \frac{4}{3}\pi {r}^{3} \\ {r} = \sqrt[3]{ \frac{343 \times 3 \times 7}{4 \times 22} } \\ r = \sqrt[3]{ \frac{7203}{88} } \\ r = \sqrt[3]{81.85} = 4.34cm](https://tex.z-dn.net/?f=volume+%3D++%7B%287%29%7D%5E%7B3%7D++%3D+343+%7Bcm%7D%5E%7B3%7D++%5C%5C++%5C%5C+sphere%29+%5C%5C++%5C%5C+v+%3D++%5Cfrac%7B4%7D%7B3%7D%5Cpi+%7Br%7D%5E%7B3%7D++%5C%5C+343+%3D++%5Cfrac%7B4%7D%7B3%7D%5Cpi+%7Br%7D%5E%7B3%7D++%5C%5C++%7Br%7D++%3D++%5Csqrt%5B3%5D%7B+%5Cfrac%7B343+%5Ctimes+3+%5Ctimes+7%7D%7B4+%5Ctimes+22%7D+%7D++%5C%5C+r+%3D++%5Csqrt%5B3%5D%7B+%5Cfrac%7B7203%7D%7B88%7D+%7D++%5C%5C+r+%3D++%5Csqrt%5B3%5D%7B81.85%7D++%3D+4.34cm "volume = {(7)}^{3} = 343 {cm}^{3} \\ \\ sphere) \\ \\ v = \frac{4}{3}\pi {r}^{3} \\ 343 = \frac{4}{3}\pi {r}^{3} \\ {r} = \sqrt[3]{ \frac{343 \times 3 \times 7}{4 \times 22} } \\ r = \sqrt[3]{ \frac{7203}{88} } \\ r = \sqrt[3]{81.85} = 4.34cm")
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