A metal cube of edge $12\ cm$ is melted and formed into three smaller cubes. If the edges of the two smaller cubes are $6\ cm$ and $8\ cm$, find the edge of the third smaller cube.

Given:

A metal cube of edge $12\ cm$ is melted and formed into three smaller cubes.

The edges of the two smaller cubes are $6\ cm$ and $8\ cm$.

To do:

We have to find the edge of the third smaller cube.

Solution:

Edge of the metal cube $= 12\ cm$

Volume of the cube $= (12)^3$

$= 1728\ cm^3$

Edge of the first smaller cube $= 6\ cm$

Edge of the second smaller cube $= 8\ cm$

Volume of the two smaller cubes $= (6)^3 + (8)^3$

$= 216 + 512$

$= 728\ cm^3$

This implies,

Volume of the third smaller cube $= 1728 - 728$

$= 1000\ cm^3$

Edge of the third smaller cube $= \sqrt[3]{1000}$

$= 10\ cm$

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Updated on: 10-Oct-2022

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