Question

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

Answer 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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