Question

A metal sheet 27 cm long, 4 cm broad and 2 cm thick is melted into a cube. The difference between the surface area of two solids is

• A. $184c{m}^2$
• B. $150c{m}^2$
• C. $124c{m}^2$
• D. $130c{m}^2$

Answer 1

The correct option is C $124c{m}^2$

Length of cuboid$=27cm$
Breadth of cuboid$=4cm$
Height of cuboid$=2cm$
$\therefore$ Surface area of cuboid$=2(27\times 4+4\times 2+2\times )=340c{m}^2$
$\therefore$ Volume of cuboid$=27\times 4\times 2=216c{m}^3$
But, Volume of cube $=$ Volume of cuboid$=216c{m}^3$
$\therefore$ $l^3=216$
$\therefore$$l=6cm$
Surface area of cube$=6l^2=216c{m}^2$
Hence, Difference between the surface area of two solids is$=340-216=124c{m}^2$