# 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

### 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
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.