Three metal cubes with edges $6\ cm, 8\ cm$ and $10\ cm$ respectively are melted together and formed into a single cube. Find the volume, surface area and diagonal of the new cube.

Given:

Three metal cubes with edges $6\ cm, 8\ cm$ and $10\ cm$ respectively are melted together and formed into a single cube.

To do:

We have to find the volume, surface area and diagonal of the new cube.

Solution:

Edge of the first cube $= 6\ cm$

Edge of the second cube $= 8\ cm$

Edge of the third cube $= 10\ cm$

Therefore,

Volume of three cubes $= (6)^3 + (8)^3 + (10)^3$

$= 216 + 512 + 1000$

$= 1728\ cm^3$

Edge of the cube so formed $=\sqrt[3]{(1728)}$

$=\sqrt[3]{(12)^{3}}$

$=12 \mathrm{~cm}$

Surface area of the cube $=6(\mathrm{side})^{2}$

$=6 \times 12 \times 12$

$=864 \mathrm{~cm}^{3}$

This implies,

Length of the diagonal $=\sqrt{3} \times  side$

$=\sqrt{3} \times 12$

$=12 \sqrt{3} \mathrm{~cm}$

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Updated on: 10-Oct-2022

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