Volume of a Cube

Volume of 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
 Volume of a Cube (V) = l × l × l = l3

Workout Examples

Example 1: Find the volume of the given solid figure.
Example 1: Cube
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   
l = square root of 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                                
l = cube root of 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.

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