Question

A metallic box is in the shape of solid having dimensions 200cm*50cm*100cm.it is recast into solid cube.find the differences of surface area of two solids

Answer 1

We know that the volume of a cuboid = l x b x h
Therefore, volume of metallic box = 200 x 50 x 100
= 1000000cm³

Now, when the box is recasted into a cube, the volume will remain the same. So, the volume of the cuboid formed = 1000000cm³. Thus, it each side
= ∛1000000
=  100cm

Total surface area of the cuboid = 2(lb + bh + hl)
= 2(200 x 50 + 50 x 100 + 100 x 200)
= 2(10000 + 5000 + 20000)
= 2 x 35000
= 70000cm²

Total surface area of the cube = 6a²
= 6 x 100 x 100
= 60000cm²

Difference in their surface areas
= 70000 - 60000
= 10000cm²

Hope that helps !!

Answer 2

volume of cube = volume of cuboid
a³ = lbh
a³ = 200×50×100
a³ = 1000000
a=100cm
so, tsa of cuboid = 2(lb+bh+hl)
                          = 2(200×50+50×100+100×200)
                          = 2(10000+5000+20000)
                          = 2(35000)
                          = 70000cm²
tsa of cube = 6a²
                  = 6(100)²
                  = 60000cm²
then differences in their sa's = 70000-60000
                                          = 10000cm²