Question

Threee cubes of the same metals, whose edges are 6,8,10 cm are melted and formed into a single cube. find the diagonal of these single cube.

Answer 1

As we know that the volume of cube $\left(V\right)$ is given by,

$V=a^3$

where as, $a$ is the side of cube

Volume of cube of edge $6cm,\left(V_1\right)=6^3=216{cm}^3$

Volume of cube of edge $8cm,\left(V_2\right)=8^3=512{cm}^3$

Volume of cube of edge $10cm,\left(V_3\right)={\left(10\right)}^3=100{cm}^3$

Total volume of the single cube formed $\left(V^{\prime }\right)=V_1+V_2+V_3=216+512+1000=1728{cm}^3$

Let $a^{\prime }$ be the edge of single cube formed.

$\therefore V^{\prime }={\left(a^{\prime }\right)}^3$

$\Rightarrow a^{\prime }=\sqrt[3]{31728}=12cm$

Now as we know that the length of diagonal $\left(d\right)$ of a cube of edge $a$ is given as-

$d=\sqrt{3}a$

$\therefore$ Length of diagonal of the single cube formed $=\sqrt{3}\times 12=20.784cm$

Hence the correct answer is $20.784cm$.