Answer:
Since, surface area of cube \[=\text{ }150\text{ }{{m}^{2}}\] Let the length of each edge = a Then, surface area of cube = 6a2 According to problem, \[6{{a}^{2}}=150\] or \[{{a}^{2}}=\frac{150}{6}=25\] or \[{{a}^{2}}=\text{ }25\] \[\Rightarrow a=\text{ }\sqrt{25\text{ }}=\text{ }\sqrt{5\times 5}\] \[\Rightarrow a=\text{ }5\text{ }m\] We know that, Volume of cube \[={{a}^{3}}\] cubic metre Therefore, Volume of cube \[=\text{ }{{5}^{3}}\] \[=\text{ }5\text{ }\times \text{ }5\text{ }\times \text{ }5\] \[=\text{ }125\text{ }{{m}^{3}}\]
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