SURFACE AREA OF A CUBE

- November 15, 2024

On my first day of my micro teaching practice, the topic i chosen is "SURFACE AREA OF A CUBE".

CUBE:

     A cube is a solid having six square faces. In other words, a cuboid whose length, breadth and height are all equal is called as a cube. A cube being a cuboid has 6 faces, 12 edges and 8 vertices. 

Example: Dice, Ice cubes, Rubik's cube etc...

SURFACE AREA - DEFINITION:

    The area occupied by a three-dimensional object by its outer surface is called the surface area. It is measured in square units.

Generally, Surface area can be of two types:

•  Total Surface Area
•  Curved Surface Area/Lateral Surface Area

Total Surface Area:

    

    Total Surface Area (TSA) of a cuboid is the sum of the areas of all the faces that enclose the cuboid.

Lateral Surface Area:

    Lateral Surface Area (LSA) is the area of sides of three-dimensional object, excluding the top and the bottom.

Now we move on to study about the surface area of a cube! 

Consider a cube whose sides are ‘a’ units. 

(i) Total Surface Area of the cube

           

             = sum of area of the faces (ABCD+EFGH+AEHD+BFGC+ABFE+CDHG) 

           

             = a²+ a²+ a²+ a²+ a²+ a²

           

             = 6a² sq. units

(ii) Lateral Surface Area of the cube

             = sum of area of the faces (AEHD+BFGC+ABFE+CDHG) 

             = a²+ a²+ a²+ a²

            = 4a² sq. units 

Thus, If the side of a cube is a units, then, 

            (i) The Total Surface Area = 6a² sq. units 

            (ii) The Lateral Surface Area = 4a² sq. units 

Let us see some problems based on this concept. 

Example: 1

Find the Total Surface Area and Lateral Surface Area of the cube, whose side is 5 cm.

Solution:

Given, the side of the cube (a) = 5 cm

Total Surface Area = 6a² = 6(5)² = 150 sq. cm

Lateral Surface Area = 4a² = 4(5)² = 100 sq. cm .

Example: 2

A cube has the Total Surface Area of 486 cm². Find its lateral surface area.

Solution:

Here, Total Surface Area of the cube = 486 cm² 

That is, 6a² = 486 cm² 

            ⇒ a² = 486 /6 = 81

            ⇒ a = 9

Thus the side of  cube is 9 cm.

Therefore, Lateral Surface Area = 4a² = 4(9)² = 4x81 = 324 cm².

Now, let us solve a problem by using our critical thinking style!

Example: 3

Two identical cubes of side 7 cm are joined end to end. Find the Total and Lateral surface area of the new resulting cuboid.

Solution:

Given the side of a cube = 7 cm 

Now, Length of the resulting cuboid (l) = 7+7 =14 cm, Breadth (b) = 7 cm, 

Height (h) = 7 cm 

So, Total Surface Area = 2(lb + bh + lh) = 2× [(14x7)) + ( 7x7) + (14x7)] 

                                       = 2 x (98+49+98)

                                       = 2 x 245

                                       = 490 cm² 

Lateral Surface Area = 2 (l+b) x h

                                  = 2 x (14+7) x 7

                                  = 294 cm² 

 Thus, (i)  Total Surface Area = 490 cm²      

           (ii) Lateral Surface Area = 294 cm² .             

EVALUATION:

       1. What is meant by surface area of a three-dimensional shape?
     

       Ans: The area occupied by a three-dimensional object by its outer surface is called                          the surface area.

       

       2. Write the formula for the total and lateral surface area of a cube?

       Ans: Total Surface Area = 6a² sq. units 

               Lateral Surface Area = 4a² sq. units 

       3. If the total surface area of a cube is 2400 cm², then, find its lateral surface area.

       Ans: 1600 cm²  

         Explanation:

                Given, Total surface area of cube = 2400 cm²  

                That is, 6a² = 2400 ⇒ a² = 2400/6 = 400 

                ⇒ a = 20 cm

                Therefore, lateral surface area of cube = 4a² sq. units 

                                                                              = 4 x (20)²

                                                                              ^{= 4 x 400}

                         Therefore, Lateral surface area of cube = 1600 cm² .