Question

a metallic box is in the shape of solid cuboid having dimension 200cm x 50cm x 100cm. It is recast into a solid cube. Find the difference of surface areas of two solids.

Answer 1

volume of cuboid=lbh=200*50*100=1000000
volume of cube=a^3=1000000
a=100
surface area​ of cuboid=2(lb+bh+hl)=2(10000+5000+20000)
=70000
surface area of cube=6a*a=60000
difference=10000

Answer 2

volume of cuboid = volume of cube
volume of cuboid = length × width × height = 200 × 50 × 100 = 10^6 cm³

now , volume of cube = ( edge length) ³ = 10^6

edge length of cube = 100 cm

so,

surface area of cuboid - surface area of cube = 2( lb + bh + hl) -6×(edge length) ²
= 2( 200×50 + 50× 100+ 100× 200 ) - 6× (100)²

= 2( 10⁴ + 0.5 × 10⁴ + 2×10⁴ ) -6× 10⁴

= 10⁴ cm²