Question

Find the total surface area of a cube with a side 9 cm.

Answer 1

Hint: The area of a square is given by the formula $ A = {a^2} $ , where \[a\] is the side of the square.
We know that all the faces of a cube are square in shape. A cube has 6 faces, and surface area of one face of a cube is given by the area of square i.e. $ A = {a^2} $ . So, the total surface area of the cube would be equal to 6 times the surface area of a single face of the cube. The total surface area of the cube is given by $ 6A = 6{a^2} $ .

Complete step-by-step answer:
As shown in the figure, $ A = {a^2} $ is the area of one face of the cube.

The cube has 6 faces, so the total surface area of a cube is given by $ 6A = 6{a^2} $ , where \[a\] is the side of the cube.
The side of the cube is given as 9 cm.
To find the total surface area of the given cube, we have to substitute $ a = 9 $ in the formula.
Total surface area of the cube with side 9 cm is $ 6{\left( 9 \right)^2} = 486{\rm{ c}}{{\rm{m}}^2} $ .

Additional Information:
As per the definition given in the field of geometry, a cube is a three-dimensional solid which has 6 faces, 12 edges and 8 vertices. All the sides of the cubes are equal in length. The faces of a cube are in the form of squares.

Note: Remembering formulae becomes tedious sometimes and students often make mistakes while writing the formula for total surface area of the cube. If they understand how the formula has arrived, it would be easier for them to remember it.
There is a chance of calculation mistakes in this type of question, so handle the calculation part with care.