Question

What is the length of the side of a cube whose volume is 275 cm³. Make use of the table for the cube root.

Answer 1

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 cm³, 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:

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

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.