Volume of a cuboid

Volume of cuboid: Let there be a cuboid of length l, breadth b and height h. The area of the rectangular base ABCD of the cuboid is (l x b) . Hence,

Volume of cuboid = length x breadth x height

Illustration: A match box measures 4 cm x 2.5 cm x 1.5 cm. What will be the volume of a packet containing 12 such boxes?

Solution:  A match box is in the form of a cuboid.

Volume of one match box = 4cm x 2.5cm x 1.5cm

Volume of 12 match boxes = 12 x 15

Illustration: A cube of 9 cm edge is immersed completely in a rectangular vessel containing water. If the dimensions of the base are 15 cm and 12 cm. Find the rise in water level in the vessel.

Solution: Edge of the cube = 9 cm

So, volume of the cube =

If the cube is immersed in vessel, then the water level rises.

Let the rise in water level be x cm.

So, Volume of the cube = Volume of the water replaced by by it

Volume of the cube = Volume of the cuboid of dimension 15 cm X 12 cm X x cm

729 = 15 X 12 X x

So,

Illustration: How many 3 meter cubes can be cut from a cuboid measuring 18 m X 12 m X 9 m?

Solution: Edge of each cube = 3 m

So, volume of each cube

Volume of the cuboid = (18 X 12 X 9)

So, number of cubes

Hence 72 cubes of 3 meter can be cut from the cuboid of given dimension.