# 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.
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

### Net of a Cube

Net of a cube is as given below:

### Workout Examples

Example 1: Find the total surface area of the given solid figure.
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
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.