Question

Two cubes of side $1cm$ each, four cubes of side $2cm$ each and two cubes of side $3cm$ and $4cm$ are melted to form one cube of side.

• A. $6cm$
• B. $7cm$
• C. $8cm$
• D. $5cm$

Answer 1

The correct option is D $5cm$

Given that, two cubes of side $1cm$ each, four cubes of side $2cm$ each and two cubes of side $3cm$ and $4cm$ are melted to form one cube.

Let, the side of required cube $x$.

Now, according to question,

Volume of required cube $=$ Volume of [Two cubes of side $1cm$ each $+$ Four cubes of side $2cm$ each $+$ two cubes of side $3cm$ and $4cm$].

$⟹$ $x^3=2(1{)}^3+{4\left(2\right)}^3+3^3+4^3$

$⟹$$x^3=2+32+27+64$

$⟹$$x^3=125$

$⟹$$x=5cm$.

Hence, option $D$ is correct.