2 cubes each of volume 64 cm3 are joined end to end. Find the surface area of the resulting cuboid.


Answer :


Let the length of each edge of the cube be a cm.

Then, Volume \( = \ 64 \)cm3

\( \Rightarrow \ a^3 \ = \ 64 \ \)
\( \Rightarrow \ a \ = \ 4 \) cm

When two cubes of equal volumes (i.e., equal edges) are joined end to end, we get a cuboid such that its,

l = Length \( = \ 4 \ + \ 4 \ = \ 8 \) cm

b = Breadth = 4 cm

and h = Height = 4 cm

\(\therefore \) Surface area of the cuboid = 2(lb + bh + hl)

\( = \ 2(8 \ × \ 4 \ + \ 4 \ × \ 4 \ + \ 4 \ × \ 8) \)

\(= 2(32 \ + \ 16 \ + \ 32) \)

\(= (2 \ × \ 80) \)

\(= \ 160 \) cm2

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