Question

a mettalic box is in the shape of solid cuboid having dimensions 200*50*100cm it is recasting into a solid cube find the difference of surface areas of two solids

Answer 1

volume of the solid cuboid = 200×50×100 = 1000000 cm³
now, volume of the solid cube = volume of the solid cuboid
⇒(side)³= 1000000 cm³
⇒side = ∛1000000 = 100 cm
surface area of cuboid= 2(200×50)+2(50×100) +2(200×100)
                                   =20000 +10000+40000
                                   = 70000 cm³
surface area of cube = 6(100)² = 60000 cm²
difference in area = (70000 - 60000) = 10000 cm²

Answer 2

volume of cuboid = volume of cube.... because cube is formed from same cuboid.
200*50*100 = (side)^3
1000000 = (side)^3
cube of side on other side becomes cube root....
so..
100 cm= side
sur. ar.of cuboid
= 2 (lb+bh+hl)
=2(200*50+50*100+100*200)
2(10000+5000+20000)...
2(35000)= 70000cm2
sur. ar of cube= 6 (a×a)
=6(100*100)
= 6 (10000)
= 60000cm2
difference of their surface areas= area of cuboid - area of cube.
=70000-60000 cm2
= 10000 cm2.