if total surface area of cube is 1014,find the lateral surface area and main diagonal of the cube​

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1. Solution

   Given :–

   • Total surface area of cube = 1014 .

   Find :–

   • Lateral surface area of cube
   • Diagonal of cube

   Explanation

   Using Formula

   ★ Total surface area of cube = 6a²

   Where,

   • a = side .

   So, Now

   ==> Total surface area of cube = 6a²

   ==> 1014 = 6a²

   ==> a² = 1014/6

   ==> a² = 169

   ==> a = ±√169

   ==> a = ±13

   But, we know,

   Length be always positive .

   Then, take .

   • a = 3 .

   Again, calculate Lateral surface area of cube.

   Using Formula

   ★Lateral surface area of cube = 4a²

   keep value of side(a).

   ==> Lateral surface area of cube = 4×(3)²

   ==> Lateral surface area of cube = 4×9

   ==> Lateral surface area of cube = 36 unit ².

   Now, Calculate diagonal of cube.

   Using Formula

   ★Diagonal of cube = √3 a.

   Keep value of a ,

   ==> Diagonal of cube =√3(3)

   ==> Diagonal of cube = 3√3 . units.

   Hence

   • Side of cube = 3 unut
   • Lateral surface area of cube = 36 unit²
   • Diagonal of cube = 3√3 units.

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