Total Surface Area of Cube

Total Surface Area of Cube

Total Surface Area of Cube

A cube is a solid object having six square faces of equal length (l). Area of each square face is l2. Therefore the total surface area (TSA) of a cube is 6l2.
Total surface area (TSA) of a cube
There are 12 edges in a cube. Therefore, the perimeter of a cube is 12l, and the latreal surface area (LSA) i.e. area of 4 faces (walls) is 4l2.

Volume of cube = l3


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Net of a Cube

Net of a cube is as given below:
Net of Cube

Workout Examples

Example 1: Find the total surface area of the given solid figure.
Example 1: Cube
Solution: The given solid figure is a cube of length (l) 8cm,
                  T.S.A. of cube = 6l2
                                             = 6 × (8cm)2
                                             = 6 × 64 cm2
                                             = 384 cm2

Example 2: The total surface area of a cubical box is 216cm2. Find the length of the box.
Solution: Here,
                  T.S.A. of cubical box = 216cm2
                  i.e.           6l2 = 216
                  or,           l2 = 216/6
                  or,           l2 = 36          

                 or,           l = 6cm

Example 3: If the volume of cubical block is 1728cm3, Find:
a.     The length of its each edge.
b.     The total surface area of the block.
c.     The cost of painting its all edges at Rs. 50 per cm2.
Solution: Here,
                  Volume of cubical block = 1728cm3
                  i.e.         l3 = 1728           
l = cube toot of 1728
                  or,          l = 12cm

    a.    length of each edge = 12cm

    b.  T.S.A. of block = 6l2
                 = 6 × (12cm)2
                 = 6 × 144cm2
                 = 864cm2

    c.  Rate of painting = Rs. 50 per cm2
   ∴  Cost of painting = Rate × Area
                                    = Rs. 50 × 864
                                    = Rs. 43200  

You can comment your questions or problems regarding area and volume of cubes here.