Question

A metal sheet $27cm$ long, $8cm$ broad and $1cm$ thick is melted into a cube. The side of the cube is

(a) $6cm$ (b) $8cm$ (c) $23cm$ (d) $24cm$

Answer 1

Correct option is (a) $6cm$

Given, a metal sheet $27cm$ long, $8cm$ broad and $1cm$ thick.
Then, volume of the sheet (cuboidal) $=l\times b\times h$
$=27\times 8\times 1=216c{m}^3$
Now, since this sheet is melted to form a cube of edge length $a$ (say).
Then, volume of the cube = Volume of the metal sheet
$\Rightarrow a^3=216c{m}^3$
$\Rightarrow a=6cm$
Hence, the side of the cube is $6cm$.