Question

3 Cube, each having an edge 4 cm are joined together. find the surface area of the cuboid thus formed. is this surface area equal to the sum of the surface areas of the three separate cubes?

Answer 1

Dear Student,
Solution) Given - 3 cubes of edge 4cm are joined end to end. Now, if we combine three cubes of edges, then
Length of cuboid = 4 + 4 + 4 = 12cm
Breadth and height = 4cm
As, we know that,
Total surface area of cuboid = 2(lb+bh+lh)
= 2(12×4+4×4+12×4)
= 2(48+16+48)
​​​​​ = 2(112)
= 224cm^​​2 ...(i)
$$\begin{gathered} Now,surfaceareaofcube=6{\left(side\right)}^2=6{\left(4\right)}^2=6\times 4\times 4=96c{m}^2 \\ Sumof3surfaceareaofcube=3\times 96c{m}^2=288c{m}^2.......\left(ii\right) \\ Therefore,from\left(i\right)and\left(ii\right),wecansaythat, \\ thesurfaceareaisnotequaltothesumof3surfaceareaofcube. \end{gathered}$$
Regards!