Question

If the volume of a cube is 3 root 3 a3,then total surface area of the cube is

Answer 1

Hi ,

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let the side of the cube = s units

volume of the cube = s³ cubic units -------- ( i )

Total surface area = 6s² square units ------ ( ii )
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according to the problem ,

1 ) volume of the cube = 3√3 a³ = √3 × √3 ×√3 a³ = ( √3 a )³ ----  ( iii )

     ( i ) = ( iii )

 s³ = ( √3 a )³

Therefore ,

s = √3 a units

2 ) Total Surface Area of the cube = 6s²  [ from ( ii ) ]

TSA = 6 × ( √3 a )²

        = 6 × ( √3a ) × ( √3a )

        = 6 × 3 × a²
        
        = 18a² square units

Therefore,

side of the cube = s= √3 a units

TSA = 18a² square units

I hope it helps you.

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Answer 2

Answer:

the volume of cube is =3√3a³

= √3×√3×√3a³

so as the volume of cube is √3a³

the total surface area = 6s²

                                     = 6×√3a²

                                     = 6×√3a×√3a

                                     =6×3×a²

                                     =18a²

∴hence proved

Step-by-step explanation:

i hope it may help you