Question

a metallic box is in the shape of solid cuboid having dimensions 200cm3 50cm3 100cm it is recast into a solid cube find the difference of surface areas of two solids

Answer 1

$$\begin{gathered} Dimensionsofcuboid:-200cm\times 50cm\times 100cm \\ Length\left(l\right)=200cm,breadth\left(b\right)=50cm,height\left(h\right)=100cm \\ Nowmetallicboxisrecastintoasolidcube. \\ Letabetheedgeofthecube \\ Nowvolumeofcube=volumeofcuboid \\ \Rightarrow a^3=l\times b\times h \\ \Rightarrow a^3=200cm\times 50cm\times 100cm \\ \Rightarrow a=\sqrt[3]{1000000c{m}^3} \\ \Rightarrow a=100cm \\ Nowsurfaceareaofcuboid=2(lb+bh+hl) \\ S.A_{cuboid}=2(200cm\times 50cm+50cm\times 100cm+100cm\times 200cm) \\ =2(10000c{m}^2+5000c{m}^2+20000c{m}^2) \\ =2\left(35000c{m}^2\right) \\ =70000c{m}^2 \\ Surfaceareaofcube=6a^2 \\ S.A_{cube}=6\times (100cm{)}^2=6\times 10000c{m}^2=60000c{m}^2 \\ \therefore Differenceinsurfaceareaoftwosolids=70000c{m}^2-60000c{m}^2=10000c{m}^2=1m^2 \end{gathered}$$