Question

Find the side of a cube whose volume is\[\frac{24389}{216} m^3 .\]

 

Answer 1

Volume of a cube with side s is given by: 

\[V = s^3\]

\[\therefore s = \sqrt[3]{V}\]

\[ = \sqrt[3]{\frac{24389}{216}}\]

\[ = \frac{\sqrt[3]{24389}}{\sqrt[3]{216}}\]

\[= \frac{\sqrt[3]{29 \times 29 \times 29}}{\sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3}}\]   (By prime factorisation)

\[= \frac{29}{2 \times 3}\]

\[ = \frac{29}{6}\]

Thus, the length of the side is \[\frac{29}{6} m\] .