Question

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

Answer 1

Given:-

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

To Find:-

• Total Surface Area of the Cube

Formula Used:-

• ${\boxed{\bf{Pythagoras\:theorem:\: H^2=B^2+P^2}}}$

• ${\boxed{\bf{TSA\:of\:Cube=6a^2}}}$

Solution:-

Firstly,

$\bf :\implies\: H^2=B^2+P^2$

$\bf :\implies\: (4\sqrt{3})^2=2B^2$

$\bf :\implies\: B^2=\dfrac{48}{2}$

$\bf :\implies\: B^2=24$

$\bf :\implies\: B=\sqrt{24}$

Side of the Square = √24

Now,

$\bf :\implies\:TSA\:of\:Cube=6a^2$

$\bf :\implies\:TSA\:of\:Cube=6\sqrt{24}^2$

$\bf :\implies\:TSA\:of\:Cube=6\times 24$

$\bf :\implies\:TSA\:of\:Cube=144$

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

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