Surface area of a cube is the number of square units that will exactly cover the surface of a cube. The total surface area of a cube is the sum of the areas of its surfaces. Cube is the special case of the cuboid whose faces are square of the same size and whose length, width and height are equal. The surface area of a cube is six times the surface area of one side of the cube. It unit of measurement is 'square units'.


The surface area of a cube is six times the surface area of one side of the cube. Find the surface area of one side of a cube and multiply by six. It unit of measurement is m2, cm2, inches2 etc.

Formulas:

Surface Area of a Cube = 6S2


Lateral Surface Area of a Cube = 4S2

Where 's' is the length of any edge of the cube.

The surface area is the area on the outside of a three-dimensional shape. A cube has all edges the same length, means each of the cube's six faces is a square. The total surface area is therefore six times the area of one face. Similarly, the lateral surface area of a cube is the sum of the area of the lateral faces of a cube.

Steps for Finding the Surface Area of a Cube:

1. Measure the length of any one side of the cube, because all dimensions are equal.

2. Find the surface area of one side of a cube and multiply the result by 6. (Surface Area = 6 (Side)2)

3. Write answer in the proper square unit of measurement.


Example 1:
Find the surface area of a lunch box whose shape is of a cube of edge 13 cm.

Solution:

Edge(side) of cubic lunch box = 13

Surface area of a cube = 6 side2 .

=> Surface area of a cube = 6 (132)

= 6 * 13 * 13

= 1014

Hence surface area of a lunch box is 1014 sq. cm.

Example 2:

Find the cost of painting a wooden box which is in the shape of a cube of side 10 cm at the rate of 25 cents per square cm.(Write answer in dollars)

Solution:
Step 1:
Given
Side of a cubic wooden box = 10

Step 2:

To find the cost of painting, firstly we have to find the surface area of the wooden box.

Surface area of a cube = 6 side2 .

=> Surface area of the wooden box = 6(10)2

= 6 * 10 * 10

= 600

So the surface area of the wooden box is 600 sq. cm.

Step 3:

Since cost to paint per sq. unit is 25 cents.

=> The cost of painting a wooden box = 600 * 25

= 15000 cents.

Step 4:


1 dollar = 100 cents

or 1 cent = 0.01 dollar

=> 15000 * 0.01 = 150 dollars

Hence the cost of painting a wooden box is 150 dollars.