if the length of the diagonal of a cube 4√3then let us calculate the total surface area of the cube​

1 thought on “if the length of the diagonal of a cube 4√3then let us calculate the total surface area of the cube​”

1. Given:–

   • Length of the diagonal of a cube = 4√3

   To Find:–

   • Total Surface Area of the Cube

   Formula Used:–

   • [tex]{\boxed{\bf{Pythagoras\:theorem:\: H^2=B^2+P^2}}}[/tex]

   • [tex]{\boxed{\bf{TSA\:of\:Cube=6a^2}}}[/tex]

   Solution:–

   Firstly,

   [tex]\bf :\implies\: H^2=B^2+P^2[/tex]

   [tex]\bf :\implies\: (4\sqrt{3})^2=2B^2[/tex]

   [tex]\bf :\implies\: B^2=\dfrac{48}{2}[/tex]

   [tex]\bf :\implies\: B^2=24[/tex]

   [tex]\bf :\implies\: B=\sqrt{24}[/tex]

   Side of the Square = √24

   Now,

   [tex]\bf :\implies\:TSA\:of\:Cube=6a^2[/tex]

   [tex]\bf :\implies\:TSA\:of\:Cube=6\sqrt{24}^2[/tex]

   [tex]\bf :\implies\:TSA\:of\:Cube=6\times 24[/tex]

   [tex]\bf :\implies\:TSA\:of\:Cube=144[/tex]

   Hence, The Total Surface Area of the Cube is 144 square units.

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