Question

A cube shaped box has the volume of 1 cubic meter. What is the area of one of it’s faces?

Answer 1

All of the sides are one

Answer 2

The area of one of the faces of a cube whose volume is 1 cubic meter is found being 1 sq. meter.

How to find the surface area of a cube?

A cube has all sides congruent, so its all sides have same area.

Supposing that the considered cube has side length (also called edge length) of L units.

Then, its one side's area equals  $L^2$ sq. units (as each side is a square, so we used formula for area of a square).

Since there are 6 such sides in a closed cube, thus, its surface area evaluates to

$S = L^2 + L^2 + ... + L^2 \text{\: (six times)} = 6L^2 \: \rm unit^2$

How to find the volume of a cube?

Suppose that:

The side length of the considered cube is L units.

Then, we get:

Volume of that cube = L³ cubic units.

For this case, we're specified that:

• The volume of the considered cube is 1 cubic meters.

Assume that:

The side length of the considered cube is L meters.

Then, we get:

Volume of that cube = L³ cubic meters.

But as it is 1 cubic meter, so we get:

$L^3 = 1\\\\\text{Taking cubic root of both the sides}\\\\L = \: \: ^3\sqrt{1} = 1 \: \rm m$

(Took only real roots, as length is going to be a real number, assumingly).

So, all of the sides of this cube is of 1 meters.

Each of the six faces of a cube is a square of side length = side length of that cube.

Thus, area of one of its faces = area of a square with side length 1 meter = $1 \times 1 = 1 \: \rm m^2$

Thus, the area of one of the faces of a cube whose volume is 1 cubic meter is found being 1 sq. meter.

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