A cube is a regular solid figure having six(6) square faces, eight vertices and twelve (12) edges. Each face of the cube is square shaped(having two(2) edges).

For instance, let’s take one face to be PQTW. The size of face PQTW is equal to that of each of the remaining five faces.

Area of PQTW = x × x = x²

Surface area of all six faces = 6 × x² = 6x².

Therefore, the surface area of a cube is = 6x².

**Example 1:**

Calculate the surface area of a cube whose edge is 5 cm.

** Solution**

Let the edge x = 5 cm

Surface area = 6x²

= 6 × 5 × 5 cm²

= 150 cm².

**Example 2:**

If the total surface area of a cube is 290 cm², calculate the edge.

#### **Solution**

Surface area, A = 6x²

Therefore 290 = 6x²

x² =290/6

x² = 48.3333

x = √48.3333

x = 6.95

Edge = 6.95 cm

**Example 3:**

Calculate the surface area of a cube of sugar whose edge is 10.5 cm.

#### **Solution**

The edge x = 10.5 cm

The surface area = 6x²

= 6 × 10.5 × 10.5 cm²

= 6 × 110.25 cm²

Therefore, surface area= 661.5 cm²

**Example 4:**

Calculate the edge of a cube whose total surface area is 162.7 cm².

#### **Solution**

Total surface area = 6x²

162.7 = 6x²

x² = 162.7 / 6

x² = 27.1167

x = √27.1167

x = 5.2

Edge = 5.2 cm

**Example 5:**

Calculate the surface area of a cube whose edge is 13 cm.

#### **Solution**

Surface area = 6x²

= 6 × 13 × 13 cm²

= 6 × 169 cm²

= 1,014 cm²

**Example 6:**

Calculate the edge of a cube given it’s total surface area 184 cm².

#### **Solution**

Total surface area = 6x²

184 = 6x²

x² = 184 / 6

x² = 30.6667

x = √30.6667

x = 5.537

Approximately, x = 5.54 cm

### **Exercise**

- Calculate the surface area of the following cubes with edges of:
- a) 1.8 cm
- b) 14 cm
- c) 12.5 cm
- d) 33 cm
- e) 47 cm
- Calculate the edges of the following cubes given their total surface areas:
- a) 16.8 cm²
- b) 1.625 cm²
- c) 120 cm²
- d) 353 cm²
- e) 402 cm².