Question

1.
6 cm
6 cm
Find the surface area of the cube.
Surface Area = [?] cm²
6 cm

Answer 1

Answer:

The surface area of the cube is equal to 216 cm².

General Formulas and Concepts:
Geometry

Surface Area Formula [Cube]:
$\displaystyle \text{SA} = 6a^2$

• a is a side length

Step-by-step explanation:

Step 1: Define

Identify given variables.

a = 6 cm

Step 2: Find Surface Area

1. [Surface Area Formula - Cube] Substitute in a:
   $\displaystyle \text{SA} = 6(6 \ \text{cm})^2$
2. Evaluate:
   $\displaystyle \text{SA} = \boxed{216 \ \text{cm}^2}$

∴ we have found the surface area of the cube to be 216 cm².

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Topic: Geometry

Answer 2

Part I: Recalling the surface area formula

The surface area of a 3D figure is the sum of the area of its faces.

We know the following:

1. As this shape is a cube, all faces of a cube must be a square.
2. The area of a square is known as (side)².
3. All faces in a cube must have the same area
4. There are 6 faces in a cube

Since all faces in a cube have the same area, the surface area of a cube is:

$\boxed{(\text{side})^{2} + (\text{side})^{2} + (\text{side})^{2} + (\text{side})^{2} + (\text{side})^{2} + (\text{side})x^{2} = 6(\text{side})^{2}}$

Therefore, the surface area of a cube must be known as 6(side)².

Part II: Determining the surface area of the cube

${\text{Given side length of cube:} \ |\text{6 centimeters}|$

Substitute the side length in the surface area formula and simplify:

$\implies 6(6)^{2}$

$\implies 6(6)(6)$

$\implies \boxed{216 \ \text{cm}^{2}}$

Therefore, the surface area of the cube is 216 cm².

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