Three metal cubes with edges 6cm, 8cm, 10cm respectively are melted together and formed into a single cube.
Question:
Three metal cubes with edges 6cm, 8cm, 10cm respectively are melted together and formed into a single cube. Find the volume, surface area and diagonal of the new cube.
Solution:
Let ‘a’ be the length of each edge of the new cube.
Then $a^{3}=\left(6^{3}+8^{3}+10^{3}\right) \mathrm{cm}^{3}$
$\Rightarrow a^{3}=1728$
⇒ a = 12
Therefore, Volume of the new cube $=a^{3}=1728 \mathrm{~cm}^{3}$
Surface area of the new cube $=6 \mathrm{a}^{2}=6 *(12)^{2}=864 \mathrm{~cm}^{2}$
Diagonal of the newly formed cube $=\sqrt{3} \mathrm{a}=12 \sqrt{3} \mathrm{~cm}$