# Volume of a Cube ## Volume of a Cube

Total space occupied by a cube is called the volume of that cube. A cube is a solid object having six square faces of equal size, therefore its length, breadth and height all are equal. Volume of a cube is given by the product of its length, length and length i.e length cube.
Volume of a Cube (V) = l × l × l = l3

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### Workout Examples

Example 1: Find the volume of the given solid figure.
Solution: The given solid figure is a cube of length (l) 8cm,
Volume of cube = l3
= (8cm)3
= 8cm × 8cm × 8cm
= 512 cm3

Example 2: If the total surface area of a cubical box is 486cm3, find its volume.
Solution: Here,
T.S.A. of cubical box = 486cm2
i.e.           6l2 = 486
or,           l2 = 486/6
or,           l2 = 81

or,           l = 9cm

Volume of cubical box = l3
= (9cm)3
= 9cm × 9cm × 9cm
= 729cm3

Example 3: If the volume of cubical block is 1728cm3, Find:
a.   Total surface area of the block.
b.   The cost of painting its surface at Rs. 10 per square cm.
Solution: Here,
Volume of cubical block = 1728cm3
i.e.           l3 = 1728

or,           l = 12cm

a.  Total surface area of the block = 6l2
= 6 × (12cm)2
= 6 × 144cm2
= 864cm2

b.  Rate of painting = Rs. 2 per cm2
∴  Cost of painting = Rate × Area
= Rs. 10 × 864
= Rs. 8640

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