What is the length of the side of a cube whose volume is 275 cm

Volume of a cube is given by: 

$V=a^{3}$, where $a=$ side of the cube

$\therefore$ Side of a cube $=a=\sqrt[3]{V}$

If the volume of a cube is $275 \mathrm{~cm}^{3}$, the side of the cube will be $\sqrt[3]{275}$.

We have:

$270<275<280 \Rightarrow \sqrt[3]{270}<\sqrt[3]{275}<\sqrt[3]{280}$

From the cube root table, we have: 

$\sqrt[3]{270}=6.463$ and $\sqrt[3]{280}=6.542$

For the difference $(280-270)$, i.e., 10 , the difference in values

$=6.542-6.463=0.079$

$\therefore$ For the difference $(275-270)$, i.e., 5 , the difference in values

$=\frac{0.079}{10} \times 5=0.0395 \simeq 0.04$ (upto three decimal places)

$\therefore \sqrt[3]{275}=6.463+0.04=6.503$ (upto three decimal places)

Thus, the length of the side of the cube is 6.503 cm.