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The length of the longest diagonal of a cube is 25 cm.
Calculate the total surface area of the cube.

Respuesta :

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Answer:

They diagonal through the interior of the cube is the longest. The hypotenuse is the longest side of a right triangle. The diagonal of the cube is the hypotenuse of a right angle with legs that are diagonal of a face and an edge. The edges are the shortest. They are legs of a right triangle with the diagonal of a face as the hypotenuse.

Step-by-step explanation:

sorry for answering super late

The total surface area of the cube is [tex]1250cm^{2}[/tex].

The length of longest diagonal of a cube is,

                                                       [tex]length=\sqrt{3} *side[/tex]

Given that, The length of the longest diagonal of a cube is 25 cm.

                          [tex]\sqrt{3}*side=25\\\\side=\frac{25}{\sqrt{3} }[/tex]

The total surface area of cube is, [tex]=6*(side)^{2}[/tex]

                                                        [tex]=6*(\frac{25}{\sqrt{3} } )^{2} \\\\=6*\frac{625}{3}\\\\=2*625=1250cm^{2}[/tex]

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