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 $$\frac{29}{6}m$$ .