Question

A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The side of the cube is
(a) 6 cm (b) 8 cm
(c) 23 cm (d) 24 cm

Answer 1

Given,
Length of the metal sheet = 27 cm
Breadth of the metal sheet = 8 cm
Thickness of the metal sheet = 1 cm.
So, the volume of the sheet (cuboidal)
$=l\times b\times h$
$=27\times 8\times 1=216c{m}^3$
Now this sheet is melted to form a cube.
Hence, the volume of the cube = the volume of the metal sheet.
Let the lengh of the edge of the cube formed to be $a$.
Volume of the cube = $a^3$.
Now, $a^3=216c{m}^3$
$\Rightarrow a=6cm$
Hence, the side of the cube formed is 6 cm.