Volume of Cuboid

Volume of Cuboid

Total space occupied by a cuboid is called the volume of cuboid. Volume of cuboid is given by the product of its area of base and the height of the cuboid. Area of base is given by the product of its length and breadth. So the volume of cuboid is given simply by the product of its length, breadth and height. i.e.

Volume of cuboid (V) = l×b×h

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Workout Examples

Example 1: Find the volume of the given solid figure.

Solution: Here, the given solid figure is a cuboid of,

                           Length (l) = 10cm

                           Breadth (b) = 6cm

                           Height (h) = 5cm

                ∴  Volume of cuboid (V) = l × b × h

                                                         = 10cm × 6cm × 5cm

                                                         = 300cm³

Example 2: A cuboid is twice as long as its breadth and 4cm high. If its volume is 200cm³, find its length, breadth and total surface area.

Solution: Let,  breadth (b) = x

                ∴       length (l) = 2x

                and,  Height (h) = 4cm

                Volume of cuboid (V) = 200cm³

                i.e.      l × b × h = 200

                or,      2x × x × 4 = 200

                or,      8x² = 200

                or,      x² = 200/8

                or,      x² = 25

                or,      x = 5cm

                ∴ length (l) = 2x = 2 × 5cm = 10cm

                   Breadth (b) = x = 5cm

                ∴  TSA = 2 (lb + bh + lh)

                             = 2 (10×5 + 5×4 + 10×4)

                             = 2 (50 + 20 + 40)

                             = 2 × 110

                             = 220cm²

Example 3: A rectangular piece of gold is 32cm long, 16cm broad and 8cm thick. If it is melted and made a cube, find the total surface area of the cube.

Solution: Here, Length of rectangular piece of gold (l) = 32cm

                           Breadth of rectangular piece of gold (b) = 16cm

                           Height of rectangular piece of gold (h) = 8cm

                ∴ Volume of rectangular piece of gold (V) = l × b × h

                                                                                       = 32cm × 16cm × 8cm

                                                                                       = 4096cm³

                

                Since rectangular piece of gold is melted to form a cube,

                ∴ Volume of cube = Volume of rectangular piece of gold

                i.e.      l³ = 4096cm³

                or,      l³ = (16cm)³

                ∴        l = 16cm

                Now,

                          TSA of cube = 6l²

                                                = 6 × (16cm)²

                                                = 6 × 256cm²

                                                = 1536cm²

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