Cuboid

Cuboid is a solid box whose every surface is a rectangle of same area or different areas.

A cuboid will have a length, breadth and height.

Hence we can conclude that volume is 3 dimensional. To measure the volumes we need to know the measure 3 sides.

Since volume involves 3 sides it is measured in cubic units.

Units of Volume

Volume of a cuboid = (length × breadth × height) cubic units.

= (l × b × h) cubic units.

(Since area = ℓ × b)

Volume of a cuboid = area of one surface × height cubic units

Let us look at the given cuboid.

The length of the cuboid = 5 cm

The breadth of the cuboid = 3 cm

The height of cuboid (thickness) = 2 cm

The number of 1 cm cubes in the given cuboid = 30 cubes = 5 × 3 × 2

We find that volume of the given cuboid with length 5 cm, breadth 3 cm and height 2 cm is 30 cu cm.

Therefore, volume of a cuboid = length × breadth × height


Solved examples on volume of a cuboid:

1. Find the volume of a cuboid of dimensions 14 cm × 12 cm × 8 cm.

Volume of cuboid = length × breadth × height.

Here, length = 14 cm, breadth = 12 cm and height = 8 cm.

Volume of cuboid = 14 × 12 × 8 cubic cm.

= 1344 cubic cm.

Therefore, volume of cuboid = 1344 cubic cm.


2. Find the volume of a cuboid of dimensions 14 cm × 50 mm × 10 cm.

Here, length = 14 cm,

[Given, breadth = 50 mm; we need to convert breadth to same unit and then solve. We know, 10 mm = 1 cm. Therefore, 50 mm = 50/10 cm = 5 cm].

Breadth = 5 cm,

Height = 10 cm.

Volume of cuboid = length × breadth × height.

= 14 × 5 × 10

= 700 cubic cm.

Therefore, volume of cuboid = 700 cubic cm.

Note: In a cuboid, when the length, breadth and height are of different units, convert them to a same unit and then solve.


3. Find the volume of a cuboid of dimensions 17 mm × 0.2 cm × 12 mm in cu. cm.

Given, length = 17 mm.

We know, 10 mm = 1 cm.

= 17/10 cm.

= 1.7 cm.

Therefore, length = 1.7 cm.

Similarly, height = 12 mm.

We know, 10 mm = 1 cm.

= 12/10 cm.

= 1.2 cm.

Therefore, height = 1.2 cm.

Volume of cuboid = length × breadth × height.

Length = 1.7 cm, breadth = 0.2 cm and height = 1.2 cm.

= 1.7 × 0.2 × 1.2 cu. cm.

= 0.408 cu. cm.

Therefore, volume of cuboid = 0.408 cubic cm.



4. Find the number of cubical boxes of cubical side 3 cm which can be accomodated in carton of dimensions 15 cm × 9 cm × 12 cm.

Volume of box = side × side × side.

                        = 3 × 3 × 3

                        = 27 cu. cm.

Volume of carton = length × breadth × height.

                             = 15 × 9 × 12

                             = 1620 cu. cm.

Number of boxes = Volume of carton/Volume of each box.

                            = 1620/27

                            = 60

Therefore, number of cubical boxes = 60.


5. How many bricks each 25 cm long, 10 cm wide and 7.5 cm thick will be required for a wall 20 m long, 2 m high and 0.75 m thick? If bricks sell at $900 per thousand what will it cost to build the wall?

Volume of the wall = 20 m × 2 m × 0.75 m

                               = 20 × 100 cm × 2 × 100 cm × 0.75 × 100 cm

Volume of brick = 25 cm × 10 cm × 7.5 cm

Number of bricks = Volume of the wall/Volume of the brick

                            = 20 × 100 × 2 × 100 × 0.75 × 100/25 × 10 × 7.5

                            = 16000

The number of bricks = 16000

The cost of 1 thousand bricks = $ 900

The cost of building the wall = $ 900 × 16 = $ 14400

Note: While calculating the volume of a cuboid all the dimensions should be changed into the same unit. 

Volume.

Units of Volume

Cube.

Cuboid.

Practice Test on Volume.

Worksheet on Volume.



5th Grade Geometry

5th Grade Math Problems

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