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.