The largest possible sphere is carved out of a wooden solid cube of side $ 7 \mathrm{~cm} $. Find the volume of the wood left. (Use $ \pi=22 / 7 $ )

Given:

The largest possible sphere is carved out of a wooden solid cube of side \( 7 \mathrm{~cm} \).

To do:

We have to find the volume of the wood left.

Solution:

Length of the side of the solid cube $=7 \mathrm{~cm}$

This implies,

Volume of the cube $=7^3 \mathrm{~cm}^{3}$

$=343 \mathrm{~cm}^{3}$

Diameter of the largest sphere carved out $=$ Length of the side of the cube

This implies,

Diameter of the sphere carved out $=7 \mathrm{~cm}$

Radius of the sphere $r=\frac{7}{2} \mathrm{~cm}$

Volume of the sphere $=\frac{4}{3} \pi \times r^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times (\frac{7}{2})^3$

$=\frac{539}{3} \mathrm{~cm}^{3}$

Volume of wood left $=$ Volume of the cube $-$ Volume of the sphere

$=343-\frac{539}{3}$

$=\frac{1029-539}{3}$

$=\frac{490}{3}$

$=163.33 \mathrm{~cm}^{3}$

The volume of the wood left is $163.33\ cm^3$.

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Updated on: 10-Oct-2022

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