Question

if one face of a cube has an area of 6in²,what is the total surface area of the cube

Answer 1

The face of a cube is in the shape of square :

The area of one face of cube is 6 in²

i.e. Area of square = 6 in²

Since the general expression for the area of square is Side x Side

$\begin{gathered} \text{ Area of side face =6} \\ \text{side}\times side=6 \\ \text{side}^{2}=6 \\ \text{side}=\sqrt[]{6} \end{gathered}$

The general expression for the total surface area of cube is : 6 side²

Substitute the value of side :

$\begin{gathered} \text{ Total surface of area = 6 a}^{2} \\ \text{Total surface of area =6}\times(\sqrt[]{6})^2 \\ \text{Total surface of area =6}\times6 \\ \text{Total surface of area =}36in^2 \end{gathered}$

Total surface area of cube is 36 in²