Question

if the total surface area of a cube is 54 x^2. then find its lateral surface area​

Answer 1

Explanation:

Given that,

Total surface area of a cube 54x²

Let the sides of a cube be a

Since,

Total Surface Area of the cube = 6a²

→54x²=6a²

→a² = 9x²

Now,

Lateral Surface Area of the cube = 4a²

= 4*9x² = 36x²

= 4*9x² = 36x²[a² = 9x²]

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Answer 2

Answer:

if the total surface area of a cube is 54 x^2. then its lateral surface area​ is 36x²

Explanation:

Let s be the side of the cube.

A cube has six faces with equal sides.

So, the total surface area of the cube is given by:

Total Surface area = 6 × s² = 6s²

In the question, we are given the total surface area of the cube as 54x²

This means:

54x² = 6s²

Divide through by 6 to get:

9x² = s²

Getting the square root of both sides we have:

3x = s

The side of the cube is:

s = 3x

The lateral surface area of a cube is given by:

L.S.A = 4s²

This equals to:

= 4 × (3x)²

= 4 × 9x² = 36x²

The lateral surface area of the cube is therefore 36x²