What is the length of the side of a cube whose volume is $275\ cm^3$? Make use of the table for the cube root.

Given: 

Volume of a cube is $275\ cm^3$.

To find: 

We have to find the length of the side of the cube.

Solution:

Volume of the cube $=275 \mathrm{~cm}^{3}$

This implies,

Length of the side $=\sqrt[3]{\text { Volume }}$

$=\sqrt[3]{275}$

$=\sqrt[3]{27.5 \times 10}$

$\sqrt[3]{27.5}$ lies between $\sqrt[3]{27}$ and $\sqrt[3]{28}$

$\sqrt[3]{27}=3.000$

$\sqrt[3]{28}=3.037$

For the difference $(28-27)=1$,

The difference in the values $=3.037-3.000$

$=0.037$

This implies,

For the difference of $0.5$,

The difference in the values $=0.037 \times 0.5$

$=0.0185$

Therefore,

$\sqrt[3]{27.5}=3.000+0.0185$

$=3.0185$

$\sqrt[3]{10}=2.154$

Therefore,

$\sqrt[3]{275}=\sqrt[3]{27.5} \times \sqrt[3]{10}$

$=3.0185 \times 2.154$

$=6.5018$

$=6.502 \mathrm{~cm}$

The length of the side of the cube is $6.502\ cm$.

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Updated on: 10-Oct-2022

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