Two cubes each of volume 27^3cm are joined end to end to form a solid. Find the surface area. of resulting solid.

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VirαtKσhli VirαtKσhli · Answer 1 · 2022-02-10T16:33:44+01:00

Given :-

To Find :-

Solution :-

Given that the volume of cube is 27cm³ . We know that the volume of cube is given by (side)³ .

So , if we assume each side to be a , then ,

[tex]\longrightarrow[/tex] a³ = 27cm³

[tex]\longrightarrow[/tex] a = ³√{27cm³}

[tex]\longrightarrow[/tex] a = ³√3³cm³

[tex]\longrightarrow[/tex] a = 3 cm .

Hence , if we join two cubes we will get a cuboid of length 3cm + 3cm = 6cm . (l)
The breadth would be 3cm .( b)
The height would be 3cm .(h)

See attachment for figure .

And as we know that TSA of cuboid is ,

[tex]\longrightarrow[/tex]TSA = 2( lb + bh + hl )

[tex]\longrightarrow[/tex] TSA = 2 ( 6*3 + 3*3 + 3*6) cm²

[tex]\longrightarrow[/tex]TSA = 2 ( 18 +9 +18 )cm²

[tex]\longrightarrow[/tex] TSA = 2 * 45cm²

[tex]\longrightarrow[/tex] TSA = 90 cm²

Hence the new surface area of the solid is 90cm² .

I hope this helps.