Question

Діагональ куба дорівнює 6см. Знайти площу його однієї грані

Answer 1

Грані куба є квадратами. Знайдемо сторону a=d√3/3=6√3/3=2√3
S=a²=(2√3)²=12 кв. ед.

Answer 2

Finding the Area of a Cube's Face

To find the area of one face of a cube, we need to know the length of its diagonal. In this case, the diagonal of the cube is given as 6 cm.

To calculate the area of one face, we can use the formula for the area of a square, which is side length squared. Since a cube has all sides equal, the area of one face is equal to the side length squared.

Let's calculate the area of one face using the given diagonal of 6 cm.

The formula for the diagonal of a cube in terms of its side length is:

diagonal = side length * √2

We can rearrange this formula to solve for the side length:

side length = diagonal / √2

Substituting the given diagonal of 6 cm into the formula, we get:

side length = 6 cm / √2

Now, we can calculate the area of one face using the formula for the area of a square:

area of one face = side length^2

Substituting the calculated side length into the formula, we get:

area of one face = (6 cm / √2)^2

Let's simplify this expression to find the area of one face.

Using the fact that (√2)^2 = 2, we can simplify the expression as follows:

area of one face = (6 cm / √2)^2 = (6 cm)^2 / (2) = 36 cm^2 / 2 = 18 cm^2

Therefore, the area of one face of the cube is 18 square centimeters.

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