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

volume of cuboid = volume of cube
l.b.h=a³
a=∛200.50.100
a=∛1000000
a=100
side of cube = 100cm
then tsa of cube = 6a²
                          = 6.100²
                          = 60000cm²
tsa of cuboid = 2(lb+bh+hl)
                     = 2(200.50+50.100+100.200)
                     = 2(10000+5000+20000)
                     = 2(35000)
                     = 70000 cm²
and differences in their surface areas is  70000-60000=10000cm²

Answer 2

Volume of cuboid = volume of cube
l * b * h = $a^{3}$
200*50*100 = $a^{3}$
a = $\sqrt[3]{1000000}$
a = 100 cm

surface area of cube = 6 $a^{2}$
= 6 (10000) = 60000 $cm^{2}$

surface area of cuboid = 2 (lw + wh + hl)
= 2(200*50 + 50*100 + 100*200)
=2(10000 + 5000 + 20000)
=70000 $cm^{2}$

Difference in surface areas = 70000 - 60000 = 10000 $cm^{2}$