Three metal cubes with edges $15 c m, .12 c m$ and $9 c m$ . respectively are melted together and formed into a single cube. Find the diagonal of this cube.

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Solution

We know that volume does not change.
Volume of cube $= x^{3}$ where $x$ is side of cube
$\Rightarrow 15^{3} + 12^{3} + 9^{3} = a^{3}$
$a^{3} = 5832$
$a = 18 c m$
$\Rightarrow$ Diagonal of cube $= \sqrt{3} a$
$= 18 \sqrt{3}$
Hence, the answer is $18 \sqrt{3} .$

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Three metal cubes with edges 15 cm,.12 cm and 9 cm. respectively are melted together and formed into a single cube. Find the diagonal of this cube.

We know that volume does not change.Volume of cube =x3 where x is side of cube ⇒153+123+93=a3 a3=5832 a=18cm⇒ Diagonal of cube =√3a =18√3Hence, the answer is 18√3.

Three metal cubes with edges $15 c m, .12 c m$ and $9 c m$ . respectively are melted together and formed into a single cube. Find the diagonal of this cube.

We know that volume does not change.
Volume of cube $= x^{3}$ where $x$ is side of cube
$\Rightarrow 15^{3} + 12^{3} + 9^{3} = a^{3}$
$a^{3} = 5832$
$a = 18 c m$
$\Rightarrow$ Diagonal of cube $= \sqrt{3} a$
$= 18 \sqrt{3}$
Hence, the answer is $18 \sqrt{3} .$