question_answer

                           Find the volume of a cube whose surface area is 150 m2.

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

\[=\text{ }{{5}^{3}}\]

\[=\text{ }5\text{ }\times \text{ }5\text{ }\times \text{ }5\]

\[=\text{ }125\text{ }{{m}^{3}}\]