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 
∴  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 

\[= 6 . 542 - 6 . 463 = 0 . 079\]

∴  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)

∴  \[\sqrt[3]{275} = 6 . 463 + 0 . 04 = 6 . 503\]   (upto three decimal places)

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